Closed-form rectangular atomic wave functions of anN-dimensional atom

2002 ◽  
Vol 88 (2) ◽  
pp. 263-274 ◽  
Author(s):  
Shun S. Lo ◽  
Daniel A. Morales
Keyword(s):  
Closed Form ◽  
Wave Functions ◽  
Atomic Wave

scholarly journals Quantum square-well with logarithmic central spike

2018 ◽  
Vol 33 (02) ◽  
pp. 1850009 ◽  
Author(s):  
Miloslav Znojil ◽  
Iveta Semorádová
Keyword(s):  
Perturbation Theory ◽  
Boundary Conditions ◽  
Closed Form ◽  
Wave Functions ◽  
Change Of Variables ◽  
State Dependent ◽  
Square Well ◽  
Strength Formula ◽  
Schrödinger Perturbation ◽  
Dependent Interaction

Singular repulsive barrier [Formula: see text] inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction [Formula: see text] in nonlinear Schrödinger equation. In the linearized case, Rayleigh–Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small [Formula: see text] or after an amendment of the unperturbed Hamiltonian. At any spike strength [Formula: see text], the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables [Formula: see text] which interchanges the roles of the asymptotic and central boundary conditions.

Analytic Atomic Wave Functions

1932 ◽  
Vol 42 (1) ◽  
pp. 33-43 ◽  
Author(s):  
J. C. Slater
Keyword(s):  
Wave Functions ◽  
Atomic Wave

Variational Atomic Wave Functions

1939 ◽  
Vol 56 (7) ◽  
pp. 696-699 ◽  
Author(s):  
Leo Goldberg ◽  
Albert M. Clogston
Keyword(s):  
Wave Functions ◽  
Atomic Wave

A power moment reformulation of the Nikiforov–Uvarov method for exactly solvable systems

2016 ◽  
Vol 94 (4) ◽  
pp. 410-424
Author(s):  
Carlos R. Handy ◽  
Daniel Vrinceanu
Keyword(s):  
Closed Form ◽  
Discrete Spectrum ◽  
Asymptotic Form ◽  
Moment Equation ◽  
Wave Functions ◽  
Moment Equations ◽  
Power Moment ◽  
Exactly Solvable ◽  
Uvarov Method ◽  
Polynomial Expansions

Exactly solvable (ES) systems are those for which the full, discrete spectrum can be solved in closed form. In this work, we argue that a moment’s representation analysis can generate these closed-form expressions for the energy in a more direct and transparent manner than the popular Nikiforov–Uvarov (NU) procedure. NU analysis strips the asymptotic form of the physical states. We retain these to generate appropriate moment equations. We show how the form of these moment equations leads to closed-form energy expressions. The wave functions can then be generated as well. Our analysis is extendable to quasi-exactly solvable systems (QES; those for which a subset of the discrete spectrum can be generated in closed form). Two formulations are presented. One of these affirms that a previously developed, general, moment quantization procedure is exact for ES and QES states. This method is referred to as the orthogonal polynomial projection quantization method. It combines moment equation representations for physical states with weighted polynomial expansions (Handy and Vrinceanu. J. Phys. A: Math. Theor. 46, 135202 (2013). doi:10.1088/1751-8113/46/13/135202 ). We also show that in implementing any numerical search procedure to determine the quantum parameter regimes corresponding to ES or QES states, our procedure is more reliable (i.e., numerically stable) than using a Hill determinant formulation. We develop our formalism, demonstrate its effectiveness, and prove its equivalence to the NU approach for ES systems.

EXACT SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH SPHERICALLY SYMMETRIC OCTIC POTENTIAL

2012 ◽  
Vol 27 (20) ◽  
pp. 1250112 ◽  
Author(s):  
DAVIDS AGBOOLA ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Schrödinger Equation ◽  
Exact Solutions ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Spherically Symmetric ◽  
Algebraic Equations ◽  
Potential Parameters

We present exact solutions of the Schrödinger equation with spherically symmetric octic potential. We give closed-form expressions for the energies and the wave functions as well as the allowed values of the potential parameters in terms of a set of algebraic equations.

EXACT WAVE FUNCTIONS AND ENERGIES OF A NON-RELATIVISTIC FREE QUANTUM PARTICLE ON THE SURFACE OF A DEGENERATE TORUS

2004 ◽  
Vol 19 (23) ◽  
pp. 1759-1766 ◽  
Author(s):  
AXEL SCHULZE-HALBERG
Keyword(s):  
Schrödinger Equation ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Quantum Particle ◽  
Azimuthal Angle ◽  
Polar Angle ◽  
Wave Functions ◽  
Exactly Solvable

We study the non-relativistic Schrödinger equation for a free quantum particle constrained to the surface of a degenerate torus, parametrized by its polar and azimuthal angle. On restricting to wave functions that depend on the polar angle only, the Schrödinger equation becomes exactly-solvable. We compute its physical solutions (continuous, normalizable and 2π-periodic) and the associated energies in closed form.

Sign in / Sign up

Export Citation Format

Share Document