Functional integration through inverse scattering variables. II
- 15 November 1980
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 22 (10), 2400-2406
- https://doi.org/10.1103/physrevd.22.2400
Abstract
We continue to develop the method of functional integration over spectral variables introduced in a previous paper. The usual functional integration variables are taken as potentials of an auxiliary linear problem whose spectral data become new integration variables. We deal in this paper with the quantum pendulum and the one- and two-dimensional anharmonic oscillators. We find the functional integration measure and the integration bounds for the spectral variables associated with these quantum systems. This integration measure is valid semiclassically. We compute with it the functional integral for the systems mentioned before. We get in this way integral representations for the ground-state energies. These integral representations turn out to be exact in the semiclassical limit in all cases. They possess the correct large-order behavior of the perturbative expansions (both in Borel-summable and in the non-Borel-summable cases). They also exhibit correctly the tunnel-effect features.Keywords
This publication has 12 references indexed in Scilit:
- Functional integration through inverse scattering variablesPhysical Review D, 1980
- The Generalised Marchenko Equation and the Canonical Structure of the A.K.N.S.-Z.S. Inverse MethodPhysica Scripta, 1979
- Large orders in the 1/N perturbation theory by inverse scattering in one dimensionCommunications in Mathematical Physics, 1979
- Late terms in the asymptotic expansion for the energy levels of a periodic potentialPhysical Review D, 1978
- Real-time approach to instanton phenomenaNuclear Physics B, 1978
- Existence and Borel summability of resonances in hydrogen stark effectLetters in Mathematical Physics, 1978
- Coupled Anharmonic Oscillators. I. Equal-Mass CasePhysical Review D, 1973
- Coupled Anharmonic Oscillators. II. Unequal-Mass CasePhysical Review D, 1973
- Nonlinear-Evolution Equations of Physical SignificancePhysical Review Letters, 1973
- Method for Solving the Sine-Gordon EquationPhysical Review Letters, 1973