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

Journal Article · Thu Apr 01 04:00:00 EST 1976 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(76)90038-5· OSTI ID:7357965

Simon, B

We study the unique bound state which (-d/sup 2//dx/sup 2/)+lambdaV and -..delta..+lambdaV (in two dimensions) have when lambda is small and V is suitable. Our main results give necessary and sufficient conditions for there to be a bound state when lambda is small and we prove analyticity (resp. nonanalyticity) of the energy eigenvalue at lambda=0 in one (resp. two) dimensions. (AIP)

• Research Organization: Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey 08540
• OSTI ID: 7357965
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 97:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUND STATE
DIFFERENTIAL EQUATIONS
EIGENVALUES
EQUATIONS
MATHEMATICAL MODELS
NUCLEAR MODELS
ONE-DIMENSIONAL CALCULATIONS
SCHROEDINGER EQUATION
TWO-DIMENSIONAL CALCULATIONS
WAVE EQUATIONS
WEAK-COUPLING MODEL