Semiclassical quantization of the nonlinear Schrodinger equation

Journal Article · Sat Jan 31 23:00:00 EST 1976 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(76)90191-3· OSTI ID:7364058

Nohl, C R

Using the functional integral technique of Dashen, Hasslacher, and Neveu, we perform a semiclassical quantization of the nonlinear Schrodinger equation (NLSE), which reproduces McGuire's exact result for the energy levels of the bound states of the theory. We show that the stability angle formalism leads to the one-loop normal ordering and self-energy renormalization expected from perturbation theory, and demonstrate that taking into account center-of-mass motion gives the correct nonrelativistic energy--momentum relation. We interpret the classical solution in the context of the quantum theory, relating it to the matrix element of the field operator between adjacent bound states in the limit of large quantum numbers. Finally, we quantize the NLSE as a theory of N component fermion fields and show that the semiclassical method yields the exact energy levels and correct degeneracies. (AIP)

• Research Organization: Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08540
• OSTI ID: 7364058
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 96:2; 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
ENERGY
ENERGY LEVELS
EQUATIONS
LINEAR MOMENTUM
NONLINEAR PROBLEMS
QUANTUM NUMBERS
RENORMALIZATION
SCHROEDINGER EQUATION
SELF-ENERGY
SEMICLASSICAL APPROXIMATION
WAVE EQUATIONS