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This study examines how to describe the allowed energies for particles in different situations. In the first place this study describes the allowed energies for a particle in a finite square well and subsequently the allowed energies for the electron in a hydrogen atom which will be used to prove the Rydberg formula. Afterwards this study will demonstrate the Rydberg formula experimentally, too. In the problem about the particle in a square well in a finite square well, also the time independent wave function for the particle, ?(x), will be described. In this connection this study will account for why
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