Algebraic construction of the coherent states of the Morse potential basedon supersymmetric quantum mechanics

By introducing the shape-invariant Lie algebra spanned by the supersymmetri c ladder operators plus the identity operator, we generate a discrete compl ete orthonormal basis for the quantum treatment of the one-dimensional Mors e potential. Tn this basis, which we call the pseudo-number-states, the Mor se Hamiltonian is tridiagonal. Then we construct algebraically the continuo us overcomplete set of coherent states for the Morse potential in close ana logy with the harmonic oscillator. These states coincide with a class of st ates constructed earlier by Nieto and Simmons [Phys. Rev. D 20, 1342 (1979) ] by using the coordinate representation. We also give the unitary displace ment operator creating these coherent states from the ground state. [S1050- 2947(99)50109-1].