Abstract
Exact solutions of the vibrational Schrödinger equation for a generalized potential energy function hbox {V(R)}=hbox {C}_{0}(mathrm{{R}-mathrm {R}}_{mathrm{e}})^{2}/[hbox {aR},+,(mathrm{{b}-mathrm {a}})hbox {R}_{mathrm{e}}]^{2} are obtained. It includes those of Dunham, Ogilvie and Simons–Parr–Finlan potentials as special cases corresponding to b = 1, a = 0, 1/2, 1, respectively. The analytical wave functions derived are useful to test the quality of numerical methods or to perform perturbative or variational calculations for the problems that cannot be solved exactly. Coherent states for generalized potential, which minimize the position–momentum uncertainty relation are also constructed.
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