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The Physical WorldAn Inspirational Tour of Fundamental Physics$
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Nicholas Manton and Nicholas Mee

Print publication date: 2017

Print ISBN-13: 9780198795933

Published to Oxford Scholarship Online: July 2017

DOI: 10.1093/oso/9780198795933.001.0001

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Quantum Mechanics in Three Dimensions

Quantum Mechanics in Three Dimensions

Chapter:
(p.231) 8 Quantum Mechanics in Three Dimensions
Source:
The Physical World
Author(s):

Nicholas Manton

Nicholas Mee

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198795933.003.0009

In this chapter, the mathematical machinery of quantum mechanics is further developed in order to address real-world 3-dimensional physics. 3-dimensional vector notation is used for quantum mechanical operators and the Schrödinger equation is presented in this notation. The density of states of a particle in a box is considered. The angular momentum operators are defined. The eigenfunctions of the Laplacian are found. The Schrödinger equation with a spherical potential is analysed and solved for a Coulomb potential. The spectroscopy of the hydrogen atom is discussed. The spin operators are introduced. The Stern–Gerlach experiment and the Zeeman effect are discussed. The quantum mechanics of identical particles is considered and fundamental particles are shown to behave as either bosons or fermions depending on their spin. The action and the Feynman path integral are shown to offer an alternative approach to quantum mechanics that elucidates the connection between quantum and classical physics.

Keywords:   Schrödinger equation, Stern–Gerlach; spin, fermion, boson, the hydrogen atom, Feynman path integral

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