Time-dependent Schr Dinger Equation Research Articles

Derivation of Both Klein-Gordon Equation and Time Dependent Schrdinger Equation From Classical Wave Function

In this study, both of Klein-Gordon equation and time dependent Schrdinger equation are directly derived from De Broglie hypothesis (? = h=p). Besides that, a new formula of Klein- ordon equation was obtained by used two equations, i.e., the classical wave function and relativistic total energy relation hw = (h2k2)=2m+V ?. Moreover, a new equation of time dependent Schrdinger (TDSE) in three-dimension 3D was derived and evidently obtained. Thus, previous result is corresponding to (TDSE) in 3D calculated by using two equations, (i.e., Einstein energy and Newton second law of mechanics).

Exploration of electron vortices in the photoionization of diatomic molecules in intense laser fields

Based on the approach within the single-electron approximation (SEA) frame, we numerically solve the two-dimensional (2D) time-dependent Schrdinger equation of N2 molecules under co-rotating and counter-rotating circularly polarized attosecond pulses. The vortex structure appears in counter-rotating circularly laser fields rather than the co-rotating case. The calculated vortex structures corresponding to the photoionization are found to be sensitive to the time delays T d of the two pulses, laser ellipticities and carrier envelope phases (CEPs). As the ellipticity increases to 1, the momentum distribution rotates and a vortex structure appears, and the interference is proved to play an important role in momentum distribution. The vortex structures also rotate clockwisely as the relative CEPs increase. The arms of the vortex structure become longer and thinner with the increasing T d . All these phenomena can be well understood by the attosecond perturbation ionization theory and the interference effect. Our findings clarify the applicability of the SEA model of diatomic molecules in attosecond extreme-ultraviolet fields.

Trajectories of electron vortices in photoionization by bichromatic co-rotating circularly polarized laser fields

By solving the two-dimensional time-dependent Schrdinger equation (2D TDSE), we investigate the electron vortex in photoelectron momentum distribution (PMD) for He+ in bichromatic co-rotating time delayed circularly polarized laser fields. We find that the PMDs exhibit a vortex spiral structure, and the trajectories of the electron vortices are different when the emission sequence of two laser pulses changes, which is demonstrated by the trajectories of the vector potentials of two laser pulses.

Photoelectron angular distributions of H ionization in low energy regime: Comparison between different potentials**Project supported by the National Natural Science Foundation of China (Grant Nos. 11322437 and 11574010) and the National Basic Research Program of China (Grant No. 2013CB922402).

We theoretically investigate the low energy part of the photoelectron spectra in the tunneling ionization regime by numerically solving the time-dependent Schrdinger equation for different atomic potentials at various wavelengths. We find that the shift of the first above-threshold ionization (ATI) peak is closely related to the interferences between electron wave packets, which are controlled by the laser field and largely independent of the potential. By gradually changing the short-range potential to the long-range Coulomb potential, we show that the long-range potential’s effect is mainly to focus the electrons along the laser’s polarization and to generate the spider structure by enhancing the rescattering process with the parent ion. In addition, we find that the intermediate transitions and the Rydberg states have important influences on the number and the shape of the lobes near the threshold.

Frequency-domain view of nonsequential double ionization in intense laser fields

The research of laser-matter interaction has become a major direction in the field of laser physics since the invention of laser in 1960. Based on the development of the laser technique in the recent several decades, the ranges of the laser's frequency, intensity and pulse width have been explored widely. Therefore, the excitation, emission and ionization dynamic processes of a complex system in intense laser fields have been studied deeply. Especially, the nonsequential double ionization (NSDI) process has continuously attracted much attention from both experimental and theoretical sides. So far, the recollision picture is widely accepted as a dominating mechanism accounting for the NSDI process under an infrared (IR) laser field condition. This recollision picture can be classified into two mechanisms:the collision-ionization (CI) mechanism and the collision-excitation-ionization (CEI) mechanism. Recently, it is found that the NSDI process can take place in an extreme ultraviolet (XUV) laser field, and thus few-photon double ionization has been extensive studied by solving the full-dimensional time-dependent Schrdinger equation (TDSE) and the conventional nonstationary perturbation theory. This article reviews the frequency-domain theory of the NSDI processes of an atom in a monochromatic IR and IR+XUV two-color laser fields. In contrast with other approaches, such as the TDSE calculation and S-matrix method, the frequency-domain theory based on the nonperturbative quantum electrodynamics is involved in some advantages:(i) all the recollision processes, including high-order above-threshold ionization (HATI), high-order harmonic generation (HHG) and NSDI, can be dealt under the unified theoretical frame and can be decoupled into two processesa direct above-threshold ionization (ATI) followed by a laser-assisted collision (LAC) or by a laser-assisted recombination process, where these subprocesses can be investigated separately; (ii) the approach can save a lot of computation time because of its nature of time-independent. In this review, we show the different momentum spectral distributions under the CI and CEI mechanisms in the IR and IR+XUV laser fields. With the help of the channel analysis, we compare the contributions of the forward and backward collisions to the NSDI under two conditions of the monochromic IR and IR+XUV two-color laser fields. It is found that, in the CI mechanism, the backward collision makes major contribution to the NSDI in the IR laser field, while the forward collision plays a crucial role in the NSDI when the energy of the recolliding electron is very large in the IR+XUV two-color laser fields. Furthermore, by employing the saddle-point approximation, it is found that the momentum spectrum, whether in the monochromic IR or the IR+XUV two-color laser fields, is attributed to the interference between two trajectories at different saddle-point t0 and 2/1-t0 (1 is the frequency of an IR laser field) when the collision happens in each channel. On the other hand, in the CEI mechanism, the momentum spectra in the monochromic IR or the IR+XUV two-color laser fields present a distinct difference. It is further found that the momentum spectrum in the IR+XUV two-color laser fields is involved in the much more channels than that in the monochromic IR laser field, and thus the complex interference patterns in the momentum spectrum in the two-color laser fields are shown. Moreover, it is found that, in both the CI and CEI mechanisms, the XUV laser field in the NSDI not only can enhance the ionization probability of the first electron, but also can accelerate the first ionized electron so that the bound electron can gain much energy by collision, which is in favor of significant boost of the NSDI probability. This work can help people understand more deeply about the NSDI, and also may pave a way for us to continue investigating the NSDI process of complex system in intense laser fields.

Semiclassical methods for strong field ionization of atoms

As the advances of laser technology, more and more nonlinear phenomena are observed in the atoms and molecules driven by strong laser pulses. Systematic investigations on these findings, such as above threshold ionization and high-order harmonic generation, will lead us to understanding the mechanisms in the microscopic world. The most exact way to simulate the experimental measurements is to solve the time-dependent Schrdinger equation (TDSE) numerically, in which the system is described by the wave function and thus one cannot have an intuitive insight into the underling process. Therefore, several semiclassical methods have been developed to understand the strong field ionization. In the classical point of view, the electrons tunnel out when the strong laser field suppresses the Coulomb potential. Then the electrons are driven by the laser electric field according to the Newtonian equations. Semiclassical methods take into account the tunnelling of the electron, the classical orbit of the electron, and the action as the phase of trajectory, which have successfully explained main structures in the ionization spectrum. Two of the most popular semiclassical methods are the quantum trajectory Monte Carlo method and the Coulomb-corrected strong field approximation method. In the present review, we will introduce these basic methods and show how they have been developed step by step, covering the most relevant and important works in the strong field physics. Finally we give two example of applications to show how these methods work. With the advantage of the classical picture, we can identify different kind of structures in the 2D photoelectron momentum distributions and tell how the structures are formed. Nonadiabatic effects can be studied by comparing the results of the two methods, together with accurate simulation from the numerical solution of TDSE. The current semiclassical methods can be further developed into advanced ones, which can be used in more complex molecular systems or multi-electron systems, and be widely used in the study of dynamics of molecule and atoms in strong laser fields.

Multiple cutoffs in high harmonic generation via multi-XUV-photon absorption

High harmonic generation (HHG) is one of the most fundamental processes in the interaction of strong laser fields with atoms and molecules. Because of wide applications of HHG, for example, imaging atomic or molecular orbitals, visualizing chemical reactions, synthesizing a single attosecond pulse, the HHG attracts huge attentions in both theories and experiments. The HHG can be explained by the famous three-step model:first, the laser field bends the Coulomb potential and the electron tunnels out; second, the electron is accelerated in the laser field and gains kinetic energy; Third, the energetic electron recombines with the parent ion and release its energy as high energetic photons. The HHG can be tailored by controlling the each step. In this paper, we conceive a strategy to control the third step. We simulate the HHG when He+ is exposed to the combined few-cycle Ti-Sapphire (800 nm) IR femtosecond laser pulse and XUV laser pulse by numerically solving the time dependent Schrdinger equation. The simulation shows that after the electron tunnels out and gains energies from the infrared laser field, extra XUV photons may be absorbed during the electron and parent ion recombination, contributing multiple cutoffs separated by XUV photon energies in the high harmonic spectrum. This scenario is confirmed by time-delay-dependent HHG in the time-frequency representation, and by the power scaling of the cutoffs' intensities as a function of the XUV intensity.

Ionization time of He atom in the strong field tunnelling ionization mode

The question of how long it takes for a particle to tunnel through a barrier, which was first put forward by MacColl (Phys. Rev. 40 621 (1932)), belongs to the fundamental process of quantum physics and has been the subject of intense debate since then. Many efforts have been devoted to addressing this question about how to define, explain and measure this tunneling time, but widespread controversies still exist in theories and experiments. Attosecond physics offers insights into ultrafast electron dynamics in atoms and moleculars on the attosecond (10-18 s) timescales, and therefore, ionization of atoms or moleculars in a strong laser filed allows for tackling this question in an experimentally and conceptually well-defined manner. The tunneling ionization dynamics of electrons plays an extremely important role in the field, since tunneling is the first crucial step in strong field ionizations of atoms and molecules and underlies virtually all present experiments in attosecond science. In the present paper, the tunneling ionization time of a single-active electron tunneling through a He atom subjected to a step static electric field, defined as a nonvanishing positive time delay between the instant of switch-on of the step static electric field and the one of ionization, is obtained from the numerical solution of the time-dependent Schrdinger equation in one dimension. The results show that the time delay between the instant of maximum probability current at the potential barrier exit and the one of switch-on of the step static electric field and the time delay needed by the ground wave function evolving to the continuum, which can be expressed as the transition element of the incident and transmitted parts of the wave function, are both very close to the Keldysh time explained as the time it takes for the bound electron having velocity = iIp/2 to cross the tunneling barrier. Compared with the definition of tunneling time delay in other literature, the one of the ground wave function evolution to the continuous state is much consistent with the actual ionization process. The reason why the electron tunneling time cannot be defined as the time delay between the maximum ionization rate and the instant of the laser peak field is that the wave function could penetrate the tunneling barrier earlier if a few-cycle optical field is adopted in experiment. According to the analysis in this article, an experimental method of measuring the actual electron tunneling ionization time using the optical field synthesis technique is proposed. The results of this paper will be helpful in tackling the problem of tunneling time in strong ionization.

The influences of multiphoton excitation on near-threshold Harmonic emission in atoms

When an atom or a molecule interacts with an intense laser field, a coherent high-order harmonic emission is observed at a frequency that is an integer multiple magnitude of the initial frequency of the incident laser field. The harmonic emission has the characteristic of high emission efficiency at relatively high orders, and it also has a wide expansion in the frequency domain. Thus, the high-order harmonic generation can be utilized to generate coherent EUV or soft X-ray light sources as well as ultrashort at to second laser pulses. It is promising that the attosecond laser pulse will be an important tool for detecting and controlling the electron dynamics in atom and molecule systems. The mechanisms of high-order harmonics especially the high energy part of the harmonic spectrum can be explained by the well-known three-step model. The three-step model assumes that the electron in the bound state firstly are ionized by the potential barrier formed by the laser electric field and the atomic potential, then the ionized electrons oscillate in the laser field, and finally the electron with high kinetic energy gained in the laser field has the possibility to return back to the parent ion and recombines with the ground state of the system with a high energy photon emitted. As for harmonics with low orders, especially those with single photon energy near the ionization threshold, the Coulomb potential of the atom has significant influences on them. However,the effect of the Coulomb potential of the atom are not included in the three-step model, so the mechanism of near-threshold harmonics (NTH) cannot be clearly interpreted with the three-step model alone. In this circumstance, the study of the mechanism of near-threshold harmonic emission attracted people's attention in general. One important application of NTH is that it can be utilized to generate optical comb with EUV frequencies. Theoretically, Xiong et al. studied the mechanism of below-threshold harmonic (BTH) emission and found that the mechanism of this part of harmonics include the effect of the quantum-path interference and the Coulomb potential. He et al. analyzed the emission of BTH in various laser intensity regions and found that the harmonic spectrum exhibits a periodic structure as a function of the harmonic frequency when the incident laser intensity is about 1013 W/cm2. Utilizing the quantum-path and time-frequency analyses of the harmonic emission, He et al. indicated that this periodic structure can be attributed to the interference effect between two specific quantum paths. Li et al. adopted the synchrosqueezing scheme to study the near-and below-threshold harmonic emission of Cs atoms in an intense mid-infrared laser field and they showed that the multiphoton and the multiple rescattering trajectories have an effect on the NTH and BTH generation processes. Shafir et al. found that the ionic potential plays an critical role in NTH emission. Under the interaction between the atom and the intense laser field, electron in the ground state not only can be ionized but also be pumped into excited state, and these excitation processes also affect the harmonic emission. We studied the harmonic emission process near the ionization threshold by solving the time-dependent Schrdinger equation of an atom interacting with a strong laser field. Utilizing the obtained wavefunction, we systematically studied the high-order harmonic emission with the variation of the incident laser intensity. Meanwhile, through solving the TDSE with the momentum-space method, the excited-state population is precisely calculated and achieved. We show that the ninth harmonic exhibits a periodic oscillation structure with the intensity of the incident laser field increasing, and we reveals that there is a synchronous variation between the harmonic intensity and the relatively high bound state population.Within a certain range of laser intensity, the increase of the total population of the excited states corresponds to the low efficiency of harmonic emission, and this competition relationship is quite clear. Therefore, when the wavelength of the driving laser pulse is fixed, we can optimize the driving laser intensity to achieve the near-threshold harmonic emission with high efficiency.

Enhancement of high-order harmonic generation from H2+ in near plasmon-enhanced laser field

High-order harmonic generation (HHG) from the interaction among intense laserfields and atoms and molecules has attracted much attention. It is of the paramount importance and is still a rapidly growing field due to its potential to produce coherent and bright light within the uv and soft X-ray region and to generate attosecond pulses. Generally speaking, a typical spectrum of HHG shows that for the first few harmonics decrease rapidly, then present by a broad plateau of almost constant conversion efficiency, and end up with a sharp cutoff. In a recent experiment, it is verified that the field enhancement induced around the bow-tie elements with a 20-nm gap allows the generation of extremeultraviolet light directly from the output of a single femtosecond oscillator of 100-kW peak power. With the development of the HHG in the vicinity of metallic nanostructure from atomic responses, the harmonic generation in the vicinity of metallic nanostructure from molecules has also been investigated. In this paper, HHG from H2+ in bowtie-shaped nanostructure is investigated by solving the one-dimensional time-dependent Schrdinger equation within the non-Born- Oppenheimer approximation by the splitting-operator fast-Fourier transform technique. We find that the spatial position of the inhomogeneous field inside the nanostructure has a great influence on the harmonic spectrum. When the spatial position of the inhomogeneous field is translated from 30 a.u. to -30 a.u., the cutoff of the HHG can be extended and the smoother supercontinuum harmonic spectrum is formed. The underlying physical mechanism can be well demonstrated by the time-frequency distribution, the three-step model, the ionization probability and electric field of the driving laser. The harmonic order as a function of the ionization time and emission time can be given by the semi-classial three-step model. The trajectory with an earlier ionization time but a later emission time as a long electronic trajectory, and the trajectory with a later ionization time but an earlier emission time as a short electronic trajectory. The interference between the long and the short trajectories will lead to a modulated structure of the supercontinuum. When the spatial position of the inhomogeneous field is translated from 0 a.u. to 30 a.u., the cutoff of the HHG can be shortened and there are short and long electronic trajectories contributing to each harmonics and bringing about more modulations. When the spatial position of the inhomogeneous field is translated from 0 a.u. to -30 a.u., the cutoff of the HHG can be extended and there is only a short electronic trajectory contributing to each harmonics and the smoother supercontinuum harmonic spectrum is formed. The effects of the carrier-envelope phase on HHG is also demonstrated. When the carrierenvelope phase is -0.2, the cutoff of the HHG is extended. When the carrier-envelope phase is -0.2, the cutoff of the HHG is shortened. But we find that with the change of the carrier-envelope phase, their overall trends are the same, that is, the cutoff of the HHG is extended when the spatial position of the inhomogeneous field is translated from 30 a.u. to -30 a.u..

Theoretical analysis of attosecond quantum beat spectroscopy of helium excited states

SynopsisPhotoelectron spectra measured in the attosecond quantum beat spectroscopy experiment on helium were computed solving the single-electron time-dependent Schrdinger equation. Final momenta of photoelectrons were obtained from the probability flux at the boundary of the simulation region using the time-dependent surface flux (t-SURFF) method [1]. Reaching a very good agreement with the experimental results, simulations allow for deeper understanding of processes underlying the quantum beating, which-way interference and polarization of the excited state.

High-order harmonics and attosecond pulse generation of a He+ ion by a chirped two-color inhomogeneous laser field

We theoretically study high-order harmonics generation (HHG) and isolated attosecond pulse (IAP) generation in a spatially inhomogeneous chirped two-color (5 fs/800 nm and 12 fs/1600 nm) laser field by solving numerically the time-dependent Schrdinger equation(TDSE) for a one-dimensional (1D) model of He+ ion by the splitting-operator fast-Fourier transform technique. Results show that the inhomogeneity of the laser field plays an important role in the HHG process. The harmonic spectra exhibit a two-plateau structure, and the cutoff of high-order harmonics is extremely extended to 851th order and the smooth supercontinuum harmonic spectrum is obtained in a chirped two-color inhomogeneous laser field. To further understand the physical mechanism of HHG, we give a reasonable explanation for the extension of harmonic plateau by using the semi-classical three-step model, the time-frequency profile of the time-dependent dipole, and the classical electron trajectories. Explicitly, the harmonic order as a function of the ionization time and emission time can be given by the semi-classical three-step model. If we define the path with earlier ionization time and later emission time as a ongelectronic trajectory, and the path with later ionization time and earlier emission time as a short electronic trajectory, then, there exist a few electronic trajectories that contribute to the harmonics in cutoff region. Numerical results show that the short quantum path is enhanced, and the long quantum path is suppressed in spatially inhomogeneous fields, and this is advantageous to generate an IAP. We find that the quantum path can be controlled by increasing inhomogeneity parameter of the laser field. Effects of the time delay on HHG is also discussed. We find that the smooth supercontinuum harmonic spectrum is obtained by adjusting the time delay. When the time delay is t0=1.6up/1, the cutoff of the harmonics can be extended remarkably. By synthesizing the 600th to 680th (80th) order harmonics in the continuum region, an isolated 32 attosecond pulse can be generated by a spatially inhomogeneous chirped two-color laser field with parameters =0.25, =0.00105, t0=1.6/1.

Photon and photoelectron emission of the atom under the action of high-frequency laser pulse

By numerically solving the time-dependent Schrdinger equation, we investigate the ionization probability, photoelectron spectrum, and harmonic emission spectrum of the atom under the action of high-frequency laser pulses. It is found that with the increase of incident laser pulse intensity, the ionization probability of the atom first increases to a maximum value gradually and then decreases, and in this process, both the photoelectron spectrum and high-order harmonic generation spectrum change from a single-peak structure to a multi-peak one. Through the time-frequency analysis of the harmonic emission spectrum, we also find that the harmonic emission is suppressed around the pulse peak, and it occurs at the rising edge and the falling edge, which interfere with each other, thus forming the multi-peak structure. Utilizing the laws of the changes of photoelectron and harmonic spectra with incident laser pulse intensity, we can diagnose the laser intensity at which the atomic ionization suppression occurs.

Ionisation effect on the electron localisation in the subcycle waveform shaping scheme

We have theoretically studied the ionisation effect on the asymmetric dissociation of H+2 exposed to the synthesised multicycle infrared pulses of different wavelengths by solving the time-dependent Schrdinger equation without using the Born–Oppenheimer approximation. It has been demonstrated that the ionisation does slightly influence the electron localisation for the relatively low pulse intensity (less than 1014 W/cm2). However, our further results show that the ionisation effect becomes much more significant when increasing the pulse intensity, leading to a distinctly different mechanism responsible for the enhancement of the electron localisation.

Solution of the Time Dependent Schrödinger Equation and the Advection Equation via Quantum Walk with Variable Parameters

We propose a solution method of Time Dependent Schr?dinger Equation (TDSE) and the advection equation by quantum walk/quantum cellular automaton with spatially or temporally variable parameters. Using numerical method, we establish the quantitative relation between the quantum walk with the space dependent parameters and the “Time Dependent Schr?dinger Equation with a space dependent imaginary diffusion coefficient” or “the advection equation with space dependent velocity fields”. Using the 4-point-averaging manipulation in the solution of advection equation by quantum walk, we find that only one component can be extracted out of two components of left-moving and right-moving solutions. In general it is not so easy to solve an advection equation without numerical diffusion, but this method provides perfectly diffusion free solution by virtue of its unitarity. Moreover our findings provide a clue to find more general space dependent formalisms such as solution method of TDSE with space dependent resolution by quantum walk.

The dynamic process of two-electron atom irradiated by intense laser pulse using time dependent quantum Monte Carlo method

We investigate the electron dynamic process of a one-dimensional two-electron atom irradiated by strong laser pulse using the improved time-dependent quantum Monte Carlo (TDQMC) scheme. By comparison with the scheme for solving the time-dependent Schrdinger equation by using the accurate numerical integration, the dynamic variation of particle in a quantum ensemble, corresponding to the calculated wave-packet, is consistent with the evolution of time-dependent wavepacket. The computation efficiency of the TDQMC is more largely enhanced than that of the time-dependent integration method. According to the dynamic evolution behaviors of the calculated classical particle ensemble, we analyze the excitation, ionization, recombination of electron and other non-linear processes in a strong laser field.

High-oder symplectic FDTD scheme for solving time-dependent Schrdinger equation

Using three-order symplectic integrators and fourth-order collocated spatial differences, a high-order symplectic finite-difference time-domain (SFDTD(3, 4)) scheme is proposed to solve the time-dependent Schrdinger equation. First, high-order symplectic framework for discretizing the Schrdinger equation is described. The numerical stability and dispersion analyses are provided for the FDTD(2, 2), FDTD(2, 4) and SFDTD(3, 4) schemes. The results are demonstrated in terms of theoretical analyses and numerical simulations. The spatial high-order collocated difference reduces the stability that can be improved by the high-order symplectic integrators. The SFDTD(3, 4) scheme and FDTD(2, 4) approach show better numerical dispersion than the traditional FDTD(2, 2) method. The simulation results of a two-dimensional quantum well and harmonic oscillator strongly confirm the advantages of the SFDTD(3, 4) scheme over the traditional FDTD(2, 2) method and other high-order approaches. The explicit SFDTD(3, 4) scheme, which is high-order-accurate and energy-conserving, is well suited for long-term simulation.

High order harmonic generation from a two-dimensional model H atom in arbitrary polarized laser

The two-dimensional time-dependent Schrdinger equation of arbitrary polarized laser pulse interacting with a model H atom is solved by using the two-dimensional asymptotic boundary condition (ABC) and symplectic algorithm. In order to investigate the influence of ellipticity on high order harmonic generation (HHG) of atom in arbitrary polarized laser field, we consider different ellipticities, and then compute the HHG for two-dimensional model H atom. Finally, we analyze the characteristics of HHG under different polarized laser fields. So it is reasonable and effective to extend the one-dimensional ABC and symplectic algorithm to the problem of laser interacting with a two-dimensional model atom.

Single attosecond pulse generated by model helium atom exposed to the combined field of an intense few-cycle chirped laser pulse and a half cycle pulse

We propose an efficient method to generate an ultrashort attosecond pulse when a model He is exposed to the combination of an intense few-cycle chirped laser pulse and a half cycle pulse. By solving the time-dependent Schrdinger equation numerically, we find that the cut-off energy of the harmonics is extended effectively to Ip+21.6Up. By superimposing some high-order harmonics in different regions for the second plateau, the obtained pulses are all single attosecond ones. Minimum pulse achieves 37 as. Especially, by superimposing the lower order harmonics of the second plateau, one can obtain single attosecond pulse, and also the intensity of the single pulse is three order of magnitude higher than the attosecond pulse obtained near cut-off of harmonics.

两量子位Grover量子算法NMR脉冲序列参量的研究

Based on physical model of two-qubit quantum computer,two kinds of rules were proposed by solving single-body and two-body the time-dependent Schrdinger equation for designing nuclear magnetic resonance pulse sequence parameter of Grover quantum algorithm.Specified parameters were given through two kinds of designing rules and numerical simulations were carried out as specifying parameters.Results from the simulations show that target state is a pure basis state after running specified parameters by solving two-body the time-dependent Schrdinger equation and the expectation value of z-component of target state agrees with the theoretical values with a precision about 10-3.It is confirmed that rules of designing parameter is correct.