Potentials leading to an equidistant spectrum are investigated by the method of the inverse spectral problem. Using a reference potential in the form of a harmonic oscillator with a centrifugal barrier , a class of potentials with equidistant energy levels coinciding with those of the reference potential is found. New eigenfunctions are found . Asymptotic expressions are given for the potential and the wave functions. The case in which an additional level is switched on is investigated. This method of recovering the potential may also be used in the case of arbitrarily positioned energy levels.
Faculty of Physics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia
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