Transcription of Operator methods in quantum mechanics
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Operator methods in quantum mechanics
Chapter 3 Operator methods inquantum mechanicsWhile the wave mechanical formulation has proved successful in describingthe quantum mechanics of bound and unbound particles, some properties cannot be represented through a wave-like description. For example, the electronspin degree of freedom does not translate to the action of a gradient is therefore useful to reformulate quantum mechanics in a framework thatinvolves only discussing properties of operators, it is helpful to introduce a furthersimplification of notation. One advantage of the Operator algebra is that itdoes not rely upon a particular basis. For example, when one writes H= p22m,where the hat denotes an Operator , we can equally represent the momentumoperator in the spatial coordinate basis, when it is described by the differentialoperator, p= i!
the quantum mechanics of bound and unbound particles, some properties can not be represented through a wave-like description. For example, the electron spin degree of freedom does not translate to the action of a gradient operator. It is therefore useful to reformulate quantum mechanics in a framework that involves only operators.
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