- PII
- 10.31857/S0044451023070027-1
- DOI
- 10.31857/S0044451023070027
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 164 / Issue number 1
- Pages
- 23-28
- Abstract
- A new method is proposed for determining level splitting Δ in a double-well 1D potential. Two “partner” functions (one symmetric Ψ+ and the other antisymmetric Ψ–) are determined. From these functions, potentials V+(x) and V–(x) and energies and corresponding to them are determined from the Schrödinger equation. A unique property of Ψ+ and Ψ– is identity = , which makes it possible to determine Δ from the perturbation theory in parameter V+(x) – V–(x). For a double-well oscillator potential, the expression for the level splitting, which connects the instanton and single-well limits, is obtained. These results can be employed in the field theory, for which the possibility of obtaining instanton solutions from perturbation theory has been discussed more than once. A number of potentials are considered, for which the value of Δ can be determined without using the semiclassical approximation. Singular potentials of the funnel type are analyzed. The value of Δ determined in this study is compared with the results of numerical solution of the Schrödinger equation for the instanton potential.
- Keywords
- Date of publication
- 15.07.2023
- Year of publication
- 2023
- Number of purchasers
- 0
- Views
- 34
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