Operator methods in quantum mechanics
Chapter 3Operator 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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