By means of the Laplace transform and a series expansion, exact solutions of the bound state for the one-dimensional Schrödinger equation with a potential - Ze 2 / x are given. We found that the energy levels are proportional to 1/ n 2 ( n = 1,2,3,...) and the value of the wavefunction of the bound state at the origin is zero. The reasons for the wrong answer that the energy levels are proportional to ( n + ½) -2 with n an integer are analysed.
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Ran et al. (2000) studied this question.
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