If two operators act on a wave function as indicated by A Igrave B Igrave f(x), it is important to carry out the operations in succession, with the first operation being that nearest to the function Mathematically, A Igrave B Igrave f (x) A Igrave (B Igrave f(x)) and A Igrave 2 f(x) A Igrave (A Igrave f(x)) Evaluate the following successive operations A Igrave B Igrave f (x) The operators A Igrave and B Igrave are listed in the first two columns and f (x) is listed in the third column a b c d Are your answers to parts (a) and (b) are identical Are your answers to parts (c) and (d) are identical As we will learn in Chapter 17, the fact that switching the order of the operators x and d dx changes the outcome of the operation A Igrave B Igrave f (x) is the basis for the Heisenberg uncertainty principle ye y dy Ve dy

Question: If two operators act on a wave function as indicated by AÌBÌ f(x), it is important to carry out the operations in succession, with the

If two operators act on a wave function as indicated by AÌ‚BÌ‚ f(x), it is important to carry out the operations in succession, with the first operation being that nearest to the function. Mathematically, AÌ‚BÌ‚ f (x) = AÌ‚ (BÌ‚ f(x)) and AÌ‚²f(x) = AÌ‚ (AÌ‚ f(x)). Evaluate the following successive operations AÌ‚BÌ‚ f (x). The operators AÌ‚ and BÌ‚ are listed in the first two columns and f (x) is listed in the third column.

Are your answers to parts (a) and (b) are identical? Are your answers to parts (c) and (d) are identical? As we will learn in Chapter 17, the fact that switching the order of the operators x and d /dx changes the outcome of the operation AÌ‚BÌ‚ f (x) is the basis for the Heisenberg uncertainty principle.

ye y dy Ve dy

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