An Introduction to the Inverse Quantum Bound State Problem in One Dimension

A technique to reconstruct one-dimensional, reflectionless potentials and the associated quantum wave functions starting from a finite number of known energy spectra is discussed. The method is demonstrated using spectra that scale like the lowest energy states of standard problems encountered in the undergraduate curriculum such as: the infinite square well, the simple harmonic oscillator, and the one-dimensional hydrogen atom.Comment: 10 pages, 10 figures, Submitted to Am. J. Phys. August 201