Equivalence of unstable anharmonic oscillators and double wells. (English) Zbl 0817.47077

Buslaev, Vladimir; Grecchi, Vincenzo

J. Phys. A, Math. Gen. 26, No. 20, 5541-5549 (1993).

Summary: We give a direct and general proof of the equality of the energy levels of a pair of different quantum problems: the double well and the unstable anharmonic oscillator defined by complex translation. The ‘resonances’ of the two problems are also equal and are the analytic continuations of the anharmonic oscillator energy levels.

MSC:

47N50	Applications of operator theory in the physical sciences
81Q10	Selfadjoint operator theory in quantum theory, including spectral analysis

Keywords:

resonances; equality of the energy levels of a pair of different quantum problems; double well and the unstable anharmonic oscillator defined by complex translation; analytic continuations of the anharmonic oscillator energy levels