Starting with a brief introduction to the hypergeometric equations and their properties, a step-by-step method consisting of six distinct parts illustrates how to address typical problems in quantum physics in a simple and uniform fashion. This technique can also be applied to the solution of other problems, for which the Schrödinger equation can be reduced by some means to an equation of the hypergeometric type. Topics include the discrete spectrum eigenfunctions, linear harmonic oscillators, Kratzer molecular potential, and the rotational correction to the Morse formula. The text concludes with an Appendix that presents an original Fourier transform-based method for converting multicenter integrals to a single center.
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