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Abstract

According to the quantum mechanical correspondence principle, a quantum system can pass well as a classical system if the system's quantum numbers are very large. Application of the correspondence principle to some basic problems in quantum mechanics including the particle in a one-dimensional infinite well, the linear harmonic oscillator, and the two-dimensional rigid rotor is quite straightforward. However, the three-dimensional rigid rotor provides a greater challenge due to the complexity of the spherical harmonic functions that describe the rotor's angular orientation. I will explain why the seemingly classical rotation of a large rigid rotor in the xy-plane implies that quantum numbers J and MJ are equal and very large. Furthermore, I will demonstrate that the values of these quantum numbers imply a very simple spherical harmonic function that is consistent with the rotor's apparently classical behavior.

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