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**Unformatted text preview: **Prob. 3 If a Hermitian operator Q has eigenfunctions 1 and 2 with corresponding eigenvalues of a 1 and a 2 , but a 1 a 2 . Is = 1 + 2 also an eigenfunction of the operator Q ? Briefly explain. (10 pts) Prob. 4 Given a particle in the parabolic potential below, use the Ehrenfests theorem to evaluate 2 2 p dt d (15 pts) and p dt d (10 pts). 2 2 2 2 2 2 1 2 x m dx d m H +-= Prob. 5 Check if the following operators are Hermitian. A simple explanation will be sufficient and no proof necessary. ( 15 pts ) (a) ( 29 2 x ; (b) x i 2 2 -; (c) 2 2 k i -; 3...

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