scholarly journals On the semiclassical approximation to the eigenvalue gap of Schrödinger operators

2012 ◽  
Vol 389 (2) ◽  
pp. 1251-1258
Author(s):  
Duo-Yuan Chen ◽  
Min-Jei Huang
Keyword(s):  
Semiclassical Approximation ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Eigenvalue Gap

The eigenvalue gap for one-dimensional Schrödinger operators with symmetric potentials

2009 ◽  
Vol 139 (2) ◽  
pp. 359-366 ◽  
Author(s):  
Min-Jei Huang ◽  
Tzong-Mo Tsai
Keyword(s):  
Boundary Conditions ◽  
Schrödinger Operators ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Schrodinger Operators ◽  
One Dimensional ◽  
Eigenvalue Gap

We consider the eigenvalue gap for Schrödinger operators on an interval with Dirichlet or Neumann boundary conditions. For a class of symmetric potentials, we prove that the gap between the two lowest eigenvalues is maximized when the potential is constant. We also give some related results for doubly symmetric potentials.

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