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PROBLEM 1: Using the ladder operators â and â', calculate the following matrix elements Inn and Jnn' for an arbitrary relation between n and n': Inn' = (n'|a2|n), Jnn' = (n'|pr|n)

PROBLEM 1: Using the ladder operators â and â', calculate the following matrix elements Inn and Jnn' for an arbitrary relation between n and n': Inn' = (n'|a2|n), Jnn' = (n'|pr|n)

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**Problem 1:** Using the ladder operators \( \hat{a} \) and \( \hat{a}^\dagger \), calculate the following matrix elements \( I_{nn'} \) and \( J_{nn'} \) for an arbitrary relation between \( n \) and \( n' \): \[ I_{nn'} = \langle n' | x^2 | n \rangle, \quad J_{nn'} = \langle n' | px | n \rangle \]
Transcribed Image Text:**Problem 1:** Using the ladder operators \( \hat{a} \) and \( \hat{a}^\dagger \), calculate the following matrix elements \( I_{nn'} \) and \( J_{nn'} \) for an arbitrary relation between \( n \) and \( n' \): \[ I_{nn'} = \langle n' | x^2 | n \rangle, \quad J_{nn'} = \langle n' | px | n \rangle \]
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