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Quantum Mechanics for Scientists and Engineers by David A. B. Miller

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Chapter 3

The time-dependent Schrödinger equation

Prerequisite: Chapter 2.

Thus far with Schrödinger’s equation, we have considered only situations where the spatial probability distribution was steady in time. In our rationalization of the time-independent Schrödinger equation, we imagined we had, for example, a steady electron beam, where the electrons had a definite energy; this beam was diffracting off some object, such as a crystal or through a pair of slits. The result was some steady diffraction pattern (at least, the probability distribution did not vary in time). We then went on to use this equation to examine some other specific problems, including potential wells, where this requirement of definite energy led to the unusual behavior ...

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