Singular perturbations of discrete spectrum

Journal Article · Thu Sep 01 04:00:00 EDT 1988 · Sov. Phys. J. (Engl. Transl.); (United States)

DOI:https://doi.org/10.1007/BF00898228· OSTI ID:6313384

Gostev, V B; Mineev, V S; Frenkin, A R

Even solutions of the Schroedinger equation with retaining potential x/sup 2/ are constructed for singular perturbation potentials lambda absolute value x /sup -v/. It is shown that the perturbation automatically entails an induced point potential, taking account of which the perturbation matrix elements and Rayleigh-Schroedinger series may be constructed when 1 < v < 3/2. In the opposite case (3/2 less than or equal to v less than or equal to 2), although the solutions are analytic with respect to lambda, not even diverging series can be obtained for the energy solutions without solution of the Schroedinger equation. The analogy with quantum field theory is explored.

• Research Organization: M.V. Lomonosov Moscow State Univ. (USSR)
• OSTI ID: 6313384
• Journal Information: Sov. Phys. J. (Engl. Transl.); (United States), Journal Name: Sov. Phys. J. (Engl. Transl.); (United States) Vol. 31:3; ISSN SOPJA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
FIELD THEORIES
HAMILTONIANS
HARMONIC OSCILLATOR MODELS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATRIX ELEMENTS
PARITY
PARTICLE PROPERTIES
PERTURBATION THEORY
POTENTIALS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SINGULARITY