Exactness of the supersymmetric JWKB quantization formula. (English) Zbl 0726.58058
Summary: A modification of the Fröman and Fröman [N. Fröman and P. O. Fröman, JWKB Approximation: Contributions to the theory (North- Holland, Amsterdam, 1965)] technique is developed in order to study the supersymmetric JWKB formula of A. Comtet, A. Bandrauk, and D. Campbell [Phys. Lett. B 150, 159-162 (1985)]. With this modification, in a direct and nonperturbative manner, it can be proven that this quantization condition is exact for a class of solvable models.
MSC:
| 58Z05 | Applications of global analysis to the sciences |
| 81Q60 | Supersymmetry and quantum mechanics |
| 34M99 | Ordinary differential equations in the complex domain |
Keywords:
harmonic oscillator; Morse potential; ground state; Hamiltonians; supersymmetric JWKB formula; quantizationReferences:
| [1] | DOI: 10.1016/0370-2693(85)90160-1 · doi:10.1016/0370-2693(85)90160-1 |
| [2] | DOI: 10.1016/0370-2693(83)90134-X · doi:10.1016/0370-2693(83)90134-X |
| [3] | DOI: 10.1088/0305-4470/21/8/025 · doi:10.1088/0305-4470/21/8/025 |
| [4] | DOI: 10.1088/0305-4470/21/8/025 · doi:10.1088/0305-4470/21/8/025 |
| [5] | DOI: 10.1016/0370-2693(86)90049-3 · doi:10.1016/0370-2693(86)90049-3 |
| [6] | DOI: 10.1103/PhysRevA.37.2797 · doi:10.1103/PhysRevA.37.2797 |
| [7] | DOI: 10.1016/0370-2693(84)90339-3 · doi:10.1016/0370-2693(84)90339-3 |
| [8] | DOI: 10.1063/1.1664651 · doi:10.1063/1.1664651 |
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