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

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Chapter 11

Methods for one-dimensional problems

Prerequisites: Chapters 2 and 3, and for Section 11.4, Chapter 8, Sections 8.18.7.

Many interesting quantum mechanical problems can be reduced to one-dimensional mathematical problems. This reduction is often possible because the problem, though truly three-dimensional, can be mathematically separated. For example, the three-dimensional hydrogen atom also mathematically separates to leave a radial equation that looks like a one-dimensional effective Schrödinger equation. Most problems associated with electrons and planar surfaces or layered structures can be handled with one-dimensional models. Examples include field emission of electrons from planar metallic surfaces and most problems associated ...

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