Dirichlet-to-Neumann and Neumann-to-Dirichlet embedding methods for bound states of the Schrödinger equation

2004 ◽  
Vol 70 (4) ◽  
Author(s):  
Radosław Szmytkowski ◽  
Sebastian Bielski
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound States ◽  
Embedding Methods

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

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.

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.

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