CRC Press eBooks

Representation Theory

Lukong Cornelius Fai

Published Apr 19, 2022• 0 citations

Abstract

Though the wave formulation has proven successful in describing quantum mechanics, some quantum mechanical properties cannot be characterized by a wave-like description. For example, the electron spin degree of freedom cannot be translated by the action of a gradient operator and so the necessity to reformulate quantum mechanics in a framework of only operators. Note that selecting a representation implies selecting an orthonormal basis which can either be discrete or continuous in the given state space. Vectors and operators are then represented in the given basis as numbers with components imitating vectors and matrix elements imitating operators. It is worthy to note that the selection of a representation is arbitrary and of course depends on the given problem leading to the simplest algebra.

DOI: 10.1201/9781003273073-8

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