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Prove the relationship [x,px]=ih

Prove the relationship [x,px]=ih, where px =-ihd/dx. Namely, show that applying the commutator [x,px] to any function f(x) is equal to multiplying ih to f(x).

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[A,B] = A B - B A

[x,px] = x px - px x = x(-ihd/dx) - (-ihd/dx)x
= -ih x ...

Solution Summary

The expert proves the relation of a function. The commutator function is applied. The solution is given in a step-by-step equational process.