On a Schrodinger equation with periodic potential and spectrum point zero

2003 ◽  
Vol 52 (1) ◽  
pp. 109-132 ◽  
Author(s):  
Michel Willem ◽  
Wenming Zou
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Periodic Potential ◽  
Spectrum Point

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

VIII.—The Schrödinger Equation with a Periodic Potential

1971 ◽  
Vol 69 (2) ◽  
pp. 125-131
Author(s):  
M. S. P. Eastham
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Floquet Theory ◽  
Periodic Potential ◽  
Eigenvalue Problems ◽  
Alternative Proof ◽  
Conditional Stability ◽  
Image Position

SynopsisThe differential equationin N dimensions is considered, where q(x) is periodic. When N = 1, it is known that the conditional stability set coincides with the spectrum and that these also coincide with two other sets involving eigenvalues of associated eigenvalue problems. These results have been proved by means of the Floquet theory and the discriminant. Here an alternative proof is given which avoids the Floquet theory and which applies to the general case of N dimensions.

Sign in / Sign up

Export Citation Format

Share Document