Simple Wave Function Research Articles

Direct and indirect exciton states in GaAs-(Ga, Al)As double quantum wells under crossed electric and magnetic fields

A theoretical study of the direct and indirect exciton states in GaAs/Ga1-xAlxAs coupled double quantum wells under crossed electric and magnetic fields is presented. The setup of the system under consideration consists of an electric field perpendicular to the layers and an in-plane applied magnetic field. For calculations we use a variational procedure (by using a simple hydrogen-like envelope wave-function), in the effective-mass and parabolic-band approximations. Present theoretical results are found in fair agreement with available experimental measurements in double quantum well heterostructures under applied electric and magnetic fields.

Exciton diamagnetic shift in [formula omitted] quantum wells under in-plane magnetic fields

Using a variational procedure in the effective-mass and parabolic-band approximations we investigate the effects of in-plane magnetic fields on the exciton states in single GaAs/Ga1-xAlxAs quantum wells. Exciton properties are analyzed by using a simple hydrogen-like variational envelope wave-function. Present theoretical results are compared with available experimental measurements on the diamagnetic shift of the photoluminescence peak position of GaAs/Ga0.7Al0.3As quantum wells under in-plane magnetic fields [Phys. Rev. B 71 (2005) 045303].

A simple parameter-free wavefunction for the ground state of two-electron atoms

We propose a simple and pedagogical wavefunction for the ground state of two-electron atoms which (i) is parameter free, (ii) satisfies all two-particle cusp conditions, (iii) yields reasonable ground-state energies, including the prediction of a bound state for H−. The mean energy, and other mean physical quantities, is evaluated analytically. The simplicity of the result can be useful as an easy-to-use wavefunction when testing collision models.

Static properties and semileptonic decays of doubly heavy baryons in a nonrelativistic quark model

We evaluate static properties and semileptonic decays for the ground state of doubly heavy $\Xi, \Xi', \Xi^*$ and $\Omega, \Omega', \Omega^*$ baryons. Working in the framework of a nonrelativistic quark model, we solve the three--body problem by means of a variational ansazt made possible by heavy quark spin symmetry constraints. To check the dependence of our results on the inter-quark interaction we use five different quark-quark potentials that include a confining term plus Coulomb and hyperfine terms coming from one--gluon exchange. Our results for static properties (masses, charge and mass radii, magnetic moments...) are, with a few exceptions for the magnetic moments, in good agreement with a previous Faddeev calculation. Our much simpler wave functions are used to evaluate semileptonic decays of doubly heavy $\Xi,\Xi'(J=1/2)$ and $\Omega, \Omega'(J=1/2)$ baryons. Our results for the decay widths are in good agreement with calculations done within a relativistic quark model in the quark--diquark approximation.

Nucleon Meson Form Factors and Coupling Constants

The nucleon-nucleon (NN) interaction has been an object of active study for over fifty years. In the past decade high precision potentials based on one boson exchange (OBE) were developed: Argonne 18, Nijmegen '93, CD Bonn, etc. Unfortunately they are highly parametrized (≈ 40 parameters) and less theoretically sound than their predecessors: Bonn B, Nijmegen '78, Paris, etc. Historically OBE potentials parametrize the coupling constants/form factors of an effective Lagrangian. We have calculated these form factors using quark model simple harmonic oscillator wave functions and the 3P0 model of hadronic decays. We present preliminary results for phase shifts of a toy nuclear interaction model, pion (π) and scalar/iso- scalar (σ) exchange. Prospects for future work, including self-consistently extending this work to non-zero strangeness hadrons, are discussed.

Direct optimization of nodal hypersurfaces in approximate wave functions

The fixed-node variant of the diffusion quantum Monte Carlo method (FN-DMC) is capable of obtaining the exact eigenvalues (albeit numerically with statistical error) of a many-electron Hamilton operator, provided that the nodal hypersurface of the exact wave function is given. The use of nodes of a trial wave function leads to the node location error. The authors have developed local criteria to assess the accuracy of the nodes based on the distances of the nodal hypersurfaces of PsiT, TPsiT, and HPsiT which coincide for the exact wave function. These criteria are used to develop direct optimization methods for the nodal hypersurface. The optimization of the nodes is demonstrated for simple wave functions of the Be atom and the C2 molecule and verified with FN-DMC calculations.

Assignment and Extracting Dynamics from Experimentally and Theoretically Obtained Spectroscopic Hamiltonians in the Complex Spectral and Classically Chaotic Regions

An analysis of existing algebraic multiresonance spectroscopic Hamiltonians, derived by fitting to experimental data or from classical canonical or quantum Van Vleck perturbation theory, allows without any significant further classical or quantum calculation the assignment of quantum numbers and motions to states observed in spectra that were previously thought to be irregular or just unassignable. In such cases, inspection of the amplitude and phase of eigenfunctions previously calculated in the Hamiltonians derivation process but now transformed to a reduced dimension semiclassical action-angle representation reveals extremely simple albeit unfamiliar topologies that give quantum numbers by simply counting nodes and phase advances. The topology allows these simple wave functions to be sorted into dynamically different excitation ladders or classes of states which are associated with different regions of phase space. The rungs of these ladders or the states in the classes intersperse in energy causing the spectral complexity. No experimental procedure allows such sorting. The success of the work stems from (1) the qualitative insights of nonlinear dynamics, (2) the conversion of the quantum problem in full dimension to a semiclassical one in reduced dimension by use of a canonical transform that takes advantage of the polyad and other constants of the motion, and (3) the judicious choice of the reduced angle variables to reflect rational ratio resonance frequency conditions. This leads to localization of those semiclassical wave functions, which are affected by the particular resonance. In reverse, the localized appearance of the reduced dimension wave function reveals which resonances govern it and makes sorting visually simple. The success of the work also stems from (4) the revealing use of plots of phase advances as well as the usual densities of the eigenstates for sorting and assignment purposes. Even in classically chaotic regions, organizing trajectories, which correspond to averages over regional phase space structures that need not be computed, can easily be drawn as the structure about which eigenfunction localization takes place. The organizing trajectories when transformed back to the full dimensional configuration space reveal the internal molecular motions. The complexity of the usual quantum stationary and propagated wave functions and associated classical trajectories forbids most often such assignments and sorting. This procedure brings the ability to interpret complex vibrational spectra to a degree previously thought possible only for lower excitations. The new methodology replaces and extends the computationally more difficult parts of a procedure used by the authors that was applied successfully to several molecules during the past few years. The new methodology is applied to DCO, CHBrClF, and the bending of acetylene.

The longitudinal cross section of vector meson electroproduction

We analyze electroproduction of light vector mesons (V=ρ,φ and ω) at small Bjorken-x in the handbag approach, in which the process factorizes into general parton distributions and partonic subprocesses. The latter are calculated in the modified perturbative approach in which the transverse momenta of the quark and antiquark forming the vector meson are retained and Sudakov suppression is taken into account. Modeling the generalized parton distributions through double distributions and using simple Gaussian wavefunctions for the vector mesons, we compute the longitudinal cross sections at large photon virtualities. The results are in fair agreement with the findings of recent experiments performed at HERA and HERMES.

Nonradiative formation of the positron-helium triplet bound state

We have previously calculated the cross section for radiative formation of the interesting bound state consisting of a positron bound to helium, where the atomic electrons are in the triplet spin state. That process uses the metastable triplet helium system as target, and, as expected, it has a very small cross section. In this paper we examine a more probable process in which the state of interest is produced in an exchange rearrangement collision between a positronium atom and the singlet helium ground state: $\mathrm{Ps}+\mathrm{He}(^{1}S^{\mathrm{e}})\ensuremath{\rightarrow}\mathrm{Ps}{\mathrm{He}}^{+}(^{3}S^{\mathrm{e}})+{e}^{\ensuremath{-}}$. The present calculation is done in the plane-wave Born approximation, using simple initial and final wave functions and compares post and prior forms.

Effects of crossed electric and magnetic fields on the electronic and excitonic states in bulk GaAs andGaAs∕Ga1−xAlxAsquantum wells

The variational procedure in the effective-mass and parabolic-band approximations is used in order to investigate the effects of crossed electric and in-plane magnetic fields on the electronic and exciton properties in semiconductor heterostructures. Calculations are performed for bulk GaAs and $\mathrm{Ga}\mathrm{As}∕{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ quantum wells, for applied magnetic fields parallel to the layers and electric fields in the growth direction, and it is shown that the combined effects on the heterostructure properties of the applied crossed electric and magnetic fields and the direct coupling between the center-of-mass and internal exciton motions may be dealt with via a simple parameter representing the spatial distance between the centers of the electron and hole magnetic parabolas. Exciton properties are analyzed by using a simple hydrogenlike envelope excitonic wave function and present theoretical results are found in fair agreement with available experimental measurements on the diamagnetic shift of the photoluminescence peak position of $\mathrm{Ga}\mathrm{As}∕{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ quantum wells under in-plane magnetic fields.

Binding energies of excitons in symmetrical GaAs/Al0.3Ga0.7As double quantum wells

The binding energies of excitons in symmetrical GaAs/Al0.3Ga0.7As double quantum wells are calculated variationally by using a simple wave function within the effective-mass approximation. The variation of the binding energies as functions of the well and barrier width is studied. It is found that, the changing tendency of the binding energies with the well width is similar to that of the single quantum well. However, we found that the maximum value of the binding energy occurs at well size of about 10?. The well size is smaller than that in single quantum wells. The binding energies have a minimum during the increase of the barrier width, which is related to the penetration into the barrier of the wave function.

Λα, Σα and Ξα potentials derived from the [formula omitted] quark-model baryon–baryon interaction

We calculate Λα, Σα and Ξα potentials from the nuclear-matter G-matrices of the SU 6 quark-model baryon–baryon interaction. The α-cluster wave function is assumed to be a simple harmonic-oscillator shell-model wave function. A new method is proposed to derive the direct and knock-on terms of the interaction Born kernel from the hyperon–nucleon G-matrices, with explicit treatments of the nonlocality and the center-of-mass motion between the hyperon and α. We find that the SU 6 quark-model baryon–baryon interactions, FSS and fss2, yield a reasonable bound-state energy for 5 Λ He, from −3.18 to − 3.62 MeV , in spite of the fact that they give relatively large depths for the Λ single-particle potentials, 46–48 MeV, in symmetric nuclear matter. An equivalent local potential derived from the Wigner transform of the nonlocal Λα kernel shows a strong energy dependence for the incident Λ-particle, indicating the importance of the strangeness-exchange process in the original hyperon–nucleon interaction. For the Σα and Ξα potentials, we only discuss the zero-momentum Wigner transform of the interaction kernels, since these interactions turn out to be repulsive when the two isospin contributions for the ΣN and ΞN interactions are added up. These components show a strong isospin dependence: they are attractive in the isospin I = 1 / 2 ( Σα) and I = 0 ( Ξα) components and repulsive in I = 3 / 2 ( Σα) and I = 1 ( Ξα) components, which indicate that Σ and Ξ potentials could be attractive in some particular systems such as the well-known 4 Σ He system.

Nodes of entangledN-particle wave functions

In a recent paper [Bressanini et al. Phys. Rev. Lett. 95, 110201 (2005)] it was pointed out that ``the nodes of even simple wave functions are largely unexplored.'' Here we show that for $N$-particle wave functions nodal surfaces arise from the spin and orbital entanglement of constituent two-particle wave functions and derive, for two-electron atoms, 11 exact nodal rules applicable in $LS$ coupling. In addition, the ``higher symmetry'' identified numerically in the above paper is shown to be an approximate dynamical symmetry described by a molecular model or a classical unstable periodic orbit. We show that the analysis is readily extended to four-particle wave functions and consider the case of the hydrogen molecule, both fixed in space and rotating.

Correlation and asymptotic properties of muonic helium atom wavefunctions

The correlation and asymptotic properties of the wavefunctions for a muonic He atom are analysed. A simple wavefunction is developed for the ground state, incorporating these properties, which leads to an accurate value for ground state energy and hyperfine splitting for the muonic He atom. Its quality is observed to be good in terms of the local satisfaction of the Schrödinger equation. It illustrates the importance of local, structural properties of wavefunctions in the description of physical properties of atoms.

Ground state energy of charged particles clusters by quantum Monte Carlo method

Using variational and diffusion Monte Carlo methods, we have calculated the ground state energy of spinless charged particles (for N < 10) interacting through a repulsive Coulomb potential, moving in two-dimensions and kept together by an external parabolic potential. Using a very simple trial wave function, we obtain results comparable to those of a sophisticated model of a quantum dot.

Variational calculations using low-momentum potentials with smooth cutoffs

Recent variational calculations of the deuteron and the triton illustrate that simple wave function ansatze become more effective after evolving the nucleon-nucleon potential to lower momentum (``V_lowk''). However, wave function artifacts from the use of sharp cutoffs in relative momentum decrease effectiveness for small cutoffs (< 2 fm^-1) and slow down convergence in harmonic oscillator bases. These sharp cutoff artifacts are eliminated when V_lowk is generated using a sufficiently smooth cutoff regulator.

Self-interference of a single Bose–Einstein condensate due to boundary effects

A simple model wavefunction, consisting of a linear combination of two free-particle Gaussians, describes many of the observed features seen in the interactions of two isolated Bose–Einstein condensates (BECs) as they expand, overlap and interfere. It is shown that a simple extension of this idea can be used to predict the qualitative time-development of a single expanding BEC produced near an infinite wall boundary, giving similar interference phenomena. Other possible time-dependent behaviours of single BECs in restricted geometries, such as wave packet revivals are also briefly discussed.

The strangeness form factors of the proton

The present empirical information on the strangeness form factors indicates that the corresponding uudss¯ component in the proton is such that the uuds subsystem has the flavor spin symmetry [4]FS[22]F[22]S and mixed orbital symmetry [31]X. This uudss¯ configuration leads to the empirical signs of all the form factors GEs,GMs and GAs. An analysis with simple quark model wave functions for the preferred configuration shows that the qualitative features of the empirical strangeness form factors may be described with a ∼15% admixture of uudss¯ with a compact wave function in the proton. Transition matrix elements between the uud and uudss¯ components give significant contributions.

Second-order correction to perfect pairing: An inexpensive electronic structure method for the treatment of strong electron-electron correlations

We have formulated a second-order perturbative correction for perfect-pairing wave functions [PP2] based on similarity-transformed perturbation techniques in coupled cluster theory. The perfect-pairing approximation is used to obtain a simple reference wave function which can qualitatively describe bond breaking, diradicals, and other highly correlated systems, and the perturbative correction accounts for the dynamical correlation. An efficient implementation of this correction using the resolution of the identity approximation enables PP2 to be computed at a cost only a few times larger than that of canonical MP2 for systems with hundreds of active electrons and tens of heavy atoms. PP2 significantly improves on MP2 predictions in various systems with a challenging electronic structure.

Determination of simple correlated wave functions for few-electron systems using a Jastrow factor

Compact Jastrow-Slater-type correlated wave functions for three- and four-electron atoms and ions (Li, ${\mathrm{Be}}^{+}$, ${\mathrm{B}}^{2+}$, ${\mathrm{C}}^{3+}$, Be, ${\mathrm{B}}^{+}$, and ${\mathrm{C}}^{2+}$) are proposed. The Jastrow factor we employed consists of one-body and two-body functions including only two variational parameters in total. We found that a one-body Jastrow function with one variational parameter, which is responsible for the screening effect around the nucleus, is effective for reproducing good total energies of the three- and four-electron atomic systems if hydrogenoid orbitals are adopted in the Slater determinant. On the other hand, a determinant composed of Hartree-Fock orbitals multiplied by the same Jastrow factor was found to give rather worse results than that composed of hydrogenoid orbitals. This result clearly indicates that analytic hydrogenoid orbitals coupled with the one-body Jastrow function are useful for describing simple wave functions and understanding the physical properties of these systems.