scholarly journals Semiclassical Limit for the Schrödinger Equation¶with a Short Scale Periodic Potential

2001 ◽  
Vol 215 (3) ◽  
pp. 609-629 ◽  
Author(s):  
Frank Hövermann ◽  
Herbert Spohn ◽  
Stefan Teufel
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Potential ◽  
Semiclassical Limit ◽  
Short Scale

scholarly journals WKB-Based Schemes for the Oscillatory 1D Schrödinger Equation in the Semiclassical Limit

2011 ◽  
Vol 49 (4) ◽  
pp. 1436-1460 ◽  
Author(s):  
Anton Arnold ◽  
Naoufel Ben Abdallah ◽  
Claudia Negulescu
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Semiclassical Limit

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

scholarly journals Dispersion Lemmas Revisited

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 365-375
Author(s):  
I. Gasser ◽  
P. A. Markowich ◽  
B. Perthame
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Semiclassical Limit ◽  
Kinetic Equations ◽  
Wigner Transform ◽  
Dirac Equations

We investigate regularizing dispersive effects for various classical equations, e.g., the Schrödinger and Dirac equations. After Wigner transform, these dispersive estimates are reduced to moment lemmas for kinetic equations. They yield new regularization results for the Schrödinger equation (valid up to the semiclassical limit) and the Dirac equation.

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