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(a) Consider the following wave function of Quantum harmonic oscillator: 3 4 V(x, t) =Vo(x)e¯REot Where, Eo, E, are the energy values corresponding to the ground state and the first excited state. Show that the expectation value of î in this state is periodic in time. What is the period? (b) Consider a quantum harmonic oscillator. The operator â4 is defined by : mw 1 â4 = 2h V2hmw Find the expectation value of Hamiltonian for the state â44,(x). [Given ,(x) = (m1/4- and p, (x) = (ma 1/4 2mw %3D nh хе %3D nh

(a) Consider the following wave function of Quantum harmonic oscillator: 3 4 V(x, t) =Vo(x)e¯REot Where, Eo, E, are the energy values corresponding to the ground state and the first excited state. Show that the expectation value of î in this state is periodic in time. What is the period? (b) Consider a quantum harmonic oscillator. The operator â4 is defined by : mw 1 â4 = 2h V2hmw Find the expectation value of Hamiltonian for the state â44,(x). [Given ,(x) = (m1/4- and p, (x) = (ma 1/4 2mw %3D nh хе %3D nh

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(a) Consider the following wave function of Quantum harmonic oscillator: 3 4 V(x, t) = =Vo(x)e¯iEot +. Where, Eo, E, are the energy values corresponding to the ground state and the first excited state. Show that the expectation value of î in this state is periodic in time. What is the period? (b) Consider a quantum harmonic oscillator. The operator â4 is defined by : mw 1 â4 = 2h d: 2ħmw Find the expectation value of Hamiltonian for the state â4,(x). ma 1/4,- x2 and , (x) = - mw ma, x2 [Given ,(x) = () mw1/4 2mw x: 1. πή
Transcribed Image Text:(a) Consider the following wave function of Quantum harmonic oscillator: 3 4 V(x, t) = =Vo(x)e¯iEot +. Where, Eo, E, are the energy values corresponding to the ground state and the first excited state. Show that the expectation value of î in this state is periodic in time. What is the period? (b) Consider a quantum harmonic oscillator. The operator â4 is defined by : mw 1 â4 = 2h d: 2ħmw Find the expectation value of Hamiltonian for the state â4,(x). ma 1/4,- x2 and , (x) = - mw ma, x2 [Given ,(x) = () mw1/4 2mw x: 1. πή
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