In this chapter we investigate the connection between quantum and classical mechanics. More precisely, taking advantage of the fact that the Planck constant provides us with a small parameter, we compute some key quantum quantities — such as quantum energy levels — in terms of relevant classical quantities. This is called quasi-classical (or semi-classical) analysis. To do this, we use the Feynman path integral representation of the evolution operator (propagator) e−iHt/ħ. This representation provides a non-rigorous but highly effective tool, as the path integral is expressed directly in terms of the key classical quantity — the classical action.
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