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VIII.—The Schrödinger Equation with a Periodic Potential

Published online by Cambridge University Press:  14 February 2012

M. S. P. Eastham
M. S. P. Eastham
Affiliation:
Department of Mathematics, Chelsea College of Science and Technology, University of London.
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Synopsis

The differential equation

in 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 69 , Issue 2 , 1971 , pp. 125 - 131
Copyright
Copyright © Royal Society of Edinburgh 1971

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References

References to Literature

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