Bound states of weakly coupled long-range one-dimensional quantum Hamiltonians

Journal Article · Thu Sep 01 04:00:00 EDT 1977 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(77)90351-7· OSTI ID:5295551

Blankenbecler, R; Goldberger, M L; Simon, B

We study the small lambda behavior of the ground state energy, E (lambda), of the Hamiltonian -(d/sup 2//dx/sup 2/)+lambdaV (x). In particular, if V (x) approx.-ax/sup -2/ at infinity and if ..integral.. V (x) dx<0, we prove that (-E (lambda))/sup 1/2/=-(1/2lambda+alambda/sup 2/ 1nlambda) ..integral.. dxV (x)+O (lambda/sup 2/).

• Research Organization: Department of Physics, Princeton University, Princeton, New Jersey 08540
• OSTI ID: 5295551
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 108:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical &amp; Mathematical Physics-- Classical &amp; Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
BOUND STATE
DIFFERENTIAL EQUATIONS
ENERGY LEVELS
EQUATIONS
HAMILTONIANS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
NUCLEAR MODELS
ONE-DIMENSIONAL CALCULATIONS
QUANTUM OPERATORS
SCHROEDINGER EQUATION
WAVE EQUATIONS
WEAK-COUPLING MODEL