Wave Functions In Momentum Space Research Articles

Gauge independent theory applied to a model of atomic ionization by an intense laser pulse

An explicitly gauge invariant strong field theory is introduced and tested using a model laser-atom interaction. The theory relies on a power series in the target potential. Transitions amplitudes are obtained by using a corresponding series in the momentum space wave function. We demonstrate that this approach is explicitly gauge invariant to all orders. A well know 1D delta function potential model is used to test the convergence of the series in the evaluation of total ionization probabilities and ionization spectra. Actually, the convergence is verified when both, the perturbation as well as the order of the expansion, are increased.

Ab initioStudy of Hyperconjugative Effect on Electronic Wavefunctions of 2-chloroethanol

The electronic structure of five conformers of 2-chloroethanol was studied by ab initio calculations at B3LYP and MP2 levels of theory with aug-cc-pVTZ basis set. The existing hydrogen bond and hyperconjugation effects on the stability of 2-chloroethanol conformers were discussed on the base of natural bond orbital analyses. The result exhibits that hyper-conjugation is the main factor to determine the stability of conformers. Such effects on the electron wavefunctions of the highest-occupied molecular orbital (HOMO) of different conformers are demonstrated with electron momentum spectroscopy, exhibiting the obviously different symmetries of the HOMO wavefunctions in momentum space.

Non-paraxial contributions to the far-field pattern of surface-emitting lasers: a manifestationof the momentum-space wavefunctions of quantum billiards

We investigated experimentally non-paraxial contributions to the high-order far-fieldpattern of large-area vertical-cavity surface-emitting lasers in order to explore by analogythe momentum-space wave distributions of quantum billiards. Our results revealthat non-paraxial contributions significantly influence the morphology of thehigh-order far-field pattern. A fast reliable method is developed for transformingthe experimental far-field patterns to the correct Fourier transform of thecorresponding near-field lasing modes. In this way we visualize the momentum-space (p–q) wavefunctions of quantum billiards.

Couplings in coupled channels versus wave functions in the case of resonances: Application to the twoΛ(1405)states

In this paper we develop a formalism to evaluate wave functions in momentum and coordinate space for the resonant states dynamically generated in a unitary coupled channel approach. The on shell approach for the scattering matrix, commonly used, is also obtained in Quantum Mechanics with a separable potential, which allows one to write wave functions in a trivial way. We develop useful relationships among the couplings of the dynamically generated resonances to the different channels and the wave functions at the origin. The formalism provides an intuitive picture of the resonances in the coupled channel approach, as bound states of one bound channel, which decays into open ones. It also provides an insight and practical rules for evaluating couplings of the resonances to external sources and how to deal with final state interaction in production processes. As an application of the formalism we evaluate the wave functions of the two $\Lambda(1405)$ states in the $\pi \Sigma$, $\bar{K} N$ and other coupled channels.

Less than perfect quantum wavefunctions in momentum-space: How ϕ(p) senses disturbances in the force

We develop a systematic approach to determine the large |p| behavior of the momentum-space wave function, ϕ(p), of a one-dimensional quantum system for which the position-space wave function, ψ(x), has a discontinuous derivative at any order. We find that if the kth derivative of the potential energy function for the system has a discontinuity, there is a corresponding discontinuity in ψ(k+2)(x) at the same point. This discontinuity leads directly to a power-law tail in the momentum-space wave function proportional to 1/pk+3. A number of familiar pedagogical examples are examined in this context, leading to a general derivation of the result.

Momentum-space engineering of gaseous Bose-Einstein condensates

We show how the momentum distribution of gaseous Bose--Einstein condensates can be shaped by applying a sequence of standing-wave laser pulses. We present a theory, whose validity for was demonstrated in an earlier experiment [L.\ Deng, et al., \prl {\bf 83}, 5407 (1999)], of the effect of a two-pulse sequence on the condensate wavefunction in momentum space. We generalize the previous result to the case of $N$ pulses of arbitrary intensity separated by arbitrary intervals and show how these parameters can be engineered to produce a desired final momentum distribution. We find that several momentum distributions, important in atom-interferometry applications, can be engineered with high fidelity with two or three pulses.

Attosecond Streaking Enables the Measurement of Quantum Phase

Attosecond streaking, as a measurement technique, was originally conceived as a means to characterize attosecond light pulses, which is a good approximation if the relevant transition matrix elements are approximately constant within the bandwidth of the light pulse. Our analysis of attosecond streaking measurements on systems with a complex response to the photoionizing pulse reveals the relation between the momentum-space wave function of the outgoing electron and the result of conventional retrieval algorithms. This finding enables the measurement of the quantum phase associated with bound-continuum transitions.

Exact Solution of D-Dimensional Klein–Gordon Oscillator with Minimal Length

Specific modifications of the usual canonical commutation relations between position and momentum operators have been proposed in the literature in order to implement the idea of the existence of a minimal observable length. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentum space representation the Klein–Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and the corresponding momentum space wave function are obtained. Following Chang et al. (Phys. Rev. D 65 (2002) 125027), we discuss constraint that can be placed on the minimal length by measuring the energy levels of an electron in a penning trap.

Exact solution of the [formula omitted]-dimensional Dirac equation with vector and scalar linear potentials in the presence of a minimal length

We present an exact solution of the ( 1 + 1 ) -dimensional Dirac equation with vector and scalar linear potentials in the context of modified quantum mechanics characterized by the presence of a non-zero minimum uncertainty in position. The bound-states energy spectrum and the corresponding momentum space wavefunctions are exactly obtained. Our findings are compared with approximated results existing in the literature.

Hyperconjugative effect on the electronic wavefunctions of ethanol

Hyperconjugation is a basic conception of chemistry. Its straightforward effect is exhibited by the spatial delocalization characteristics of the electron density distributions or wavefunctions. Such effects on the electron wavefunctions of the highest-occupied molecular orbitals (HOMO) of two ethanol conformers are demonstrated with electron momentum spectroscopy together with natural bond orbital analyses, exhibiting the distinctly different symmetries of the HOMO wavefunctions in momentum space.

Covariant helicity-coupling amplitudes: A new formulation

We have worked out covariant amplitudes for any two-body decay of a resonance with an arbitrary nonzero mass, which involves arbitrary integer spins in the initial and the final states. One key new ingredient for this work is the application of the total intrinsic spin operator which is given directly in terms of the generators of the Poincar\'e group. Using the results of this study, we show how to explore the Lorentz factors which appear naturally, if the momentum-space wave functions are used to form the covariant decay amplitudes. We have devised a method of constructing our covariant decay amplitudes, such that they lead to the Zemach amplitudes when the Lorentz factors are set to one.

Mechanisms of superconductivity studied by two-particle emission

It is shown theoretically that the one-photon two-electron emission spectroscopy of superconducting surfaces provides novel information on the mechanisms of superconductivity. In particular, measured angular correlations of the photo-excited (Cooper) pairs can be related to the Cooper pair wave function in momentum space. We outline how the use of circularly polarized photons gives access to phase properties of the superconducting gap function. Furthermore, we discuss the influence of the topology of the sample and the influence of an external magnetic field for the case of superconducting rings pierced by a magnetic flux.

Hole and electron wave functions in self‐assembled InAs quantum dots: a comparison

AbstractWe have investigated the conduction and the valence band states of self‐assembled InAs quantum dots embedded in n‐ and p‐type Schottky diodes, respectively, by magneto‐capacitance voltage spectroscopy. The dispersion behaviour of the individual charging peaks in a perpendicular magnetic field shows qualitative differences between the two carrier types. By applying an in‐plane magnetic field, the momentum space wave function corresponding to the individual charging peaks could be mapped. For electrons, the s‐like wave function for the ground state is slightly asymmetric with the low energy direction along [0$ \bar 1 $1] in real space. Also the s‐like wave function for the hole ground state is asymmetric but here the low energy direction is along [011], i.e. orthogonal to that for electrons. This hints to an asymmetry in the confinement potential that is caused by piezoelectric effects. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Geometric Quantization, Parallel Transport and the Fourier Transform

In quantum mechanics, the momentum space and position space wave functions are related by the Fourier transform. We investigate how the Fourier transform arises in the context of geometric quantization. We consider a Hilbert space bundle \(\mathcal{H}\) over the space \(\mathcal{J}\) of compatible complex structures on a symplectic vector space. This bundle is equipped with a projectively flat connection. We show that parallel transport along a geodesic in the bundle \(\mathcal{H} \to \mathcal{J}\) is a rescaled orthogonal projection or Bogoliubov transformation. We then construct the kernel for the integral parallel transport operator. Finally, by extending geodesics to the boundary (for which the metaplectic correction is essential), we obtain the Segal-Bargmann and Fourier transforms as parallel transport in suitable limits.

Localization transition in a ballistic quantum wire

The many-body wave function of localized states in one dimension is probed by measuring the tunneling conductance between two parallel wires, fabricated in a $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure. Tunneling conductance in the presence of a magnetic field perpendicular to the plane of the wires serves as probe of the momentum space wave function of the wires. One of the two wires is driven into the localized regime using a density tuning gate, whereas the other wire, still in the regime of extended electronic states, serves as a momentum spectrometer. As the electron density is lowered to a critical value, the state at the Fermi level abruptly changes from an extended state with a well-defined momentum to a localized state with a wide range of momentum components. The signature of the localized states appears as discrete tunneling features at resonant gate voltages, corresponding to the depletion of single electrons and showing Coulomb-Blockade behavior. Typically 5--10 such features appear, where the one-electron state has a single-lobed momentum distribution, and the few-electron states have double-lobed distributions with peaks at $\ifmmode\pm\else\textpm\fi{}{k}_{F}$. A theoretical model suggests that for a small number of particles $(N<6)$, the observed state is a mixture of ground and thermally excited spin states.

Some aspects of gravitational quantum mechanics

String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle. Such a modified Heisenberg uncertainty principle is referred as gravitational uncertainty principle(GUP) in literatures. This proposal has some novel implications on various domains of theoretical physics. Here, we study some consequences of GUP in the spirit of Quantum mechanics. We consider two problem: a particle in an one-dimensional box and momentum space wave function for a "free particle". In each case we will solve corresponding perturbational equations and compare the results with ordinary solutions.

Wigner crystallization in inhomogeneous one-dimensional wires

We explore the theory of electrons confined by one dimensional power law potentials. We calculate the density profile in the high density electron gas, the low density Wigner crystal, and the intermediate regime. We extract the momentum space wavefunction of the electron at the Fermi surface, which can be measured in experiments on tunneling between parallel wires. The onset of localization leads to a dramatic broadening of the momentum space wavefunction together with pronounced sharpening (in energy) of the tunneling spectrum.

Electron momentum distribution in multiply-ionized neon atoms

We present momentum-space properties of multiply ionized neon atoms as a function of the degree of ionization of the atom. In particular, we have calculated the Compton profiles of all possible ionized states of neon atoms with electronic configurations 1 s m 2 s n 2 p q , m = 1 –2, n = 0 –2, q = 0 –6. The radial single-electron radial wave functions, obtained from the Hartree–Fock atomic model, were converted into momentum space wave functions by applying appropriate Fourier transformation. The values of the Compton profiles from the present calculation can be used to interpret experimental cross sections of variously ionized neon atoms colliding with other atoms. Compton profiles of neutral neon atoms, available in the literature, are in excellent agreement with the present calculation.

Magnetocapacitance probing of the many-particle states in InAs dots

We use frequency-dependent capacitance-voltage spectroscopy to measure the tunneling probability into self-assembled InAs quantum dots. Using an in-plane magnetic field of variable strength and orientation, we are able to obtain information on the quasiparticle wave functions in momentum space for one to two electrons per dot. For the lowest two energy states, we find a good agreement with Gaussian functions for a harmonic potential. The high-energy orbitals exhibit signatures of anisotropic confinement and correlation effects.

Closed-orbit theory for photodetachment ofH−in a static electric field

Standard closed-orbit theory is applied to derive the photodetachment cross section of ${\mathrm{H}}^{\ensuremath{-}}$ in the presence of a static electric field. The result agrees with the one derived earlier using a quantum approach involving a momentum-space wave function and stationary-phase approximation. The advantage of the present derivation is the ability to separate the oscillation term and the smooth background term in the photodetachment cross section and to identify the two terms with different physical origins.