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

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Chapter 5

Operators and quantum mechanics

Prerequisites: Chapters 2, 3, and 4.

In this chapter, we start to use and extend the mathematics of the previous chapter and relate it to quantum mechanics more directly.

Here, we first examine some of the important properties of operators that are associated with measurable quantities. Then, we discuss the uncertainty principle in greater mathematical detail. Finally, we introduce the δ-function, which is a very useful additional piece of mathematics, and consider some of its uses and consequences, especially in quantum mechanics.

5.1  Commutation of operators

It is considered a postulate of quantum mechanics that all measurable quantities can be associated with a Hermitian operator. We have seen the ...

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