scholarly journals Eigenvalues of the Schrödinger equation for a periodic potential with nonperiodic boundary conditions: A uniform semiclassical analysis

1984 ◽  
Vol 80 (10) ◽  
pp. 5095-5106 ◽  
Author(s):  
J. N. L. Connor ◽  
T. Uzer ◽  
R. A. Marcus ◽  
A. D. Smith
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Periodic Potential ◽  
Semiclassical Analysis

EXPECTED AND UNEXPECTED SOLUTIONS TO THE STATIONARY ONE-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1663-1667
Author(s):  
LINCOLN D. CARR ◽  
CHARLES W. CLARK ◽  
WILLIAM P. REINHARDT
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stationary Solutions ◽  
Einstein Condensate ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Bose Einstein Condensate ◽  
Dilute Gas

We present all stationary solutions to the nonlinear Schrödinger equation in one dimension for box and periodic boundary conditions. For both repulsive and attractive nonlinearity we find expected and unexpected solutions. Expected solutions are those that are in direct analogy with those of the linear Schödinger equation under the same boundary conditions. Unexpected solutions are those that have no such analogy. We give a physical interpretation for the unexpected solutions. We discuss the properties of all solution types and briefly relate them to experiments on the dilute-gas Bose-Einstein condensate.

One-Dimensional Schrödinger Equation with an Almost Periodic Potential

1983 ◽  
Vol 50 (23) ◽  
pp. 1873-1876 ◽  
Author(s):  
Stellan Ostlund ◽  
Rahul Pandit ◽  
David Rand ◽  
Hans Joachim Schellnhuber ◽  
Eric D. Siggia
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Potential ◽  
Almost Periodic ◽  
One Dimensional
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