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The bound state of weakly coupled Schrödinger operators in one and two dimensions

✍ Scribed by Barry Simon

Publisher
Elsevier Science
Year
1976
Tongue
English
Weight
443 KB
Volume
97
Category
Article
ISSN
0003-4916

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✦ Synopsis

We study the unique bound state which (-d2/dx2) + hV and -A + XV (in two dimensions) have when A is small and V is suitable. Our main results give necessary and sufficient conditions for there to be a bound state when h is small and we prove analyticity (resp. nonanalyticity) of the energy eigenvalue at X = 0 in one (resp. two) dimensions.

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