Schrödinger solution for the Morse oscillator

In his review of Ilya Kaplan’s book, Intermolecular Interactions: Physical Picture, Computational Methods, and Model Potentials (Physics Today, Physics Today 0031-9228 60 7 2007 64 https://doi.org/10.1063/1.2761808. July 2007, page 64 ), Lucjan Piela criticizes Kaplan for saying that the well-known solution of the Schrödinger equation for the Morse oscillator is approximate. The reviewer says it is exact. Actually, Kaplan is correct. The solution corresponds to an unphysical boundary condition that the wavefunction vanishes at an internuclear distance of minus infinity. The exact solution for a diatomic molecule would correspond to the wavefunction vanishing at the origin. The difference is large enough that it needs to be considered in practical work, especially for the hydrogen molecule.© 2008 American Institute of Physics.