Asymptotic estimates and Borel resummation for a doubly anharmonic oscillator

Journal Article · Fri Jun 15 00:00:00 EDT 1979 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.19.3754· OSTI ID:6246614

Sobelman, G E

The large-order behavior of perturbation theory for an oscillator with both quartic and sextic anharmonicity is examined. Two approaches are considered: an explicit double expansion in the two coupling constants and a single expansion in the number of loops. A two-variable extension of the Borel resummation technique is developed and applied to the double series, and the standard one-variable resummation technique is applied to the loop expansion. Numerical values for the ground-state energy are calculated in each case and the two procedures are compared.

• Research Organization: Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138
• OSTI ID: 6246614
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 19:12; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COUPLING CONSTANTS
ENERGY LEVELS
FIELD THEORIES
GROUND STATES
HAMILTONIANS
MATHEMATICAL OPERATORS
MECHANICS
PERTURBATION THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
SCALAR FIELDS