In several bound systems, the quantum-mechanically allowed energies depend on a single quantum number. We found in Section 5.5 that the energy levels in an infinite well are given by En=a1n2 where n = 1, 2, 3, . . . and a1, is a constant. (Actually, we know what m is, but it would only distract us here.) Section 5.7 showed that for a harmonic oscillator, they are En=a2(n-½), where n. = 1,2, 3,... . (Using an n-½)with ft strictly positive is equivalent to n +½ with n nonnegative.) Finally, for a hydrogen atom, a bound system that we study in Chapter 7, En=-a3/n2 where n = 1, 2, 3,.... Consider particles making downward transitions between the quantized energy levels, each transition producing a photon. For each of these three systems, is there a minimum photon wavelength? A maximum? It might be helpful to make sketches of the relative heights of the energy levels in each ease.
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