Gamow\u27s tunneling formula is inverted and the issue of the uniqueness of the solution is compared with the solution obtained by the method of Gel\u27fand and Levitan. Some insight is gained into the key differences between classical and quantum inverse scattering, which account for the fact that a potential can be uniquely determined in the latter but only to within a symmetry family in the former. (C) 2006 American Association of Physics Teachers
