Solution of the Schrödinger equation for bound states in closed form

1982 ◽  
Vol 26 (1) ◽  
pp. 662-664 ◽  
Author(s):  
Edgardo Gerck ◽  
Jason A. C. Gallas ◽  
Augusto B. d'Oliveira
Keyword(s):  
Schrödinger Equation ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Bound States

scholarly journals SCHRÖDINGER QUANTUM MODES ON THE TAUB–NUT BACKGROUND

2000 ◽  
Vol 15 (02) ◽  
pp. 145-157 ◽  
Author(s):  
ION I. COTĂESCU ◽  
MIHAI VISINESCU
Keyword(s):  
Schrödinger Equation ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Bound States ◽  
Conserved Quantities ◽  
Coordinate Systems ◽  
Eigenvalues And Eigenvectors

The Schrödinger equation is investigated in the Euclidean Taub–NUT geometry. The bound states are degenerate and an extra degeneracy is due to the conserved Runge–Lenz vector. The existence of the extra conserved quantities, quadratic in four-velocities implies the possibility of separating variables in two different coordinate systems. The eigenvalues and eigenvectors are given in both cases in explicit, closed form.

A class of time periodic Hamiltonians with no bound states

1987 ◽  
Vol 105 (1) ◽  
pp. 37-42
Author(s):  
H. Kaneta
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
All Solutions ◽  
Time Periodic

SynopsisWe generalise the Paley–Wiener closedness theorem and apply it to a class of time periodic Hamiltonians to show that all solutions to the corresponding Schrodinger equation decay.

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.

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