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A generation of exactly solvable anharmonic symmetric oscillators

Liu Ke-jia

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Using the ideas of supersymmetric quantum mechanics, we exactly solve a continuous family of anharmonic potentials, which are the supersymmetric partners of the linear harmonic oscillators. The family includes a series of potentials in which the excited-state energy is the same as that of the harmonic oscillators, but the ground-state energy can be any value lower than the excited states. The shape of the potential is variable, which includes the double-well and triple-well potentials. All the potentials obtained in this paper are free of singularities and the supersymmetry of the solutions is unbroken.


PACS

03.65.Ge Solutions of wave equations: bound states

Subjects

Quantum information and quantum mechanics

Dates

Issue 4 (April 2001)

Received 12 September 2000, in final form 6 December 2000



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