Algebraic construction of the coherent states of the Morse potential based on supersymmetric quantum mechanics

Mihály G. Benedict, Balázs Molnár

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By introducing the shape-invariant Lie algebra spanned by the supersymmetric ladder operators plus the identity operator, we generate a discrete complete orthonormal basis for the quantum treatment of the one-dimensional Morse potential. In this basis, which we call the pseudo-number-states, the Morse Hamiltonian is tridiagonal. Then we construct algebraically the continuous overcomplete set of coherent states for the Morse potential in close analogy with the harmonic oscillator. These states coincide with a class of states constructed earlier by Nieto and Simmons [Phys. Rev. D 20, 1342 (1979)] by using the coordinate representation. We also give the unitary displacement operator creating these coherent states from the ground state.

Original languageEnglish
Pages (from-to)R1737-R1740
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number3
Publication statusPublished - Jan 1 1999


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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