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The normalized wave functions for the ground state, po(x), and the first excited state, v,(x), of a quantum harmonic oscillator are given below where

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The normalized wave functions for the ground state, po(x), and the first excited state, v,(x), of a quantum harmonic oscillator are given below where a = mw/h: \1/4 () 4g3 1/4 do (x) = (=)e-ar"/2 W1 (2) = xe-ar/2 A mixed state, Vo1(x), is constructed from these states: vo1 (2) = The symbol < q >s denotes the expectation value of the quantity q for the state ys(x). Calculate the following expectation values. (Use the following as necessary: x and a.) (a) 0 = (b) 1 = (c) 01 =

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