An algebraic construction of the coherent states of the Morse potential\n based on SUSY QM

By introducing the shape invariant Lie algebra spanned by the SUSY ladder\noperators plus the unity operator, a new basis is presented for the quantum\ntreatment of the one-dimensional Morse potential. In this discrete, complete\northonormal set, which we call the pseudo number states, the Morse Hamiltonian\nis tridiagonal. By using this basis we construct coherent states algebraically\nfor the Morse potential, in a close analogy with the harmonic oscillator. We\nalso show that there exists an unitary displacement operator creating these\ncoherent states from the ground state. We show that our coherent states form a\ncontinuous and overcomplete set of states. They coincide with a class of states\nconstructed earlier by Nieto and Simmons by using the coordinate\nrepresentation. \\pacs{3.65.Fd, 02.20.Sv, 42.50.-p}\n