Abstract
Stationary solutions of one-dimensional hydrogen atom are two-degree degenerate. Three kinds of typical solutions can be constructed from those degenerated solutions. They correspond to three kinds of ensembles. Double-wave theory describes a single hydrogen atom. When three different averages over ensembles are made for double-wave theory, three kinds of typical solutions in the usual quantum mechanics are obtained. A comparison between these solutions and those of classical mechanics is made.
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