Suppose you have particle that is trapped in a harmonic potential V=12mω2x2. The particle is in its first excited state which has a wave function of the form ψ(x)=Axe−αx^2 where α=(mω)/(2ℏ) Normalize the wavefunction to get constant A. Compute for the expectation value of position and the expectation momentum .

Suppose you have particle that is trapped in a harmonic potential V=12mω2x2. The particle is in its first excited state which has a wave function of the form ψ(x)=Axe−αx^2 where α=(mω)/(2ℏ) Normalize the wavefunction to get constant A. Compute for the expectation value of position and the expectation momentum .

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Question

Suppose you have particle that is trapped in a harmonic potential V=12mω²x². The particle is in its first excited state which has a wave function of the form

ψ(x)=Axe^{−αx^2}

where α=(mω)/(2ℏ) Normalize the wavefunction to get constant A. Compute for the expectation value of position <x> and the expectation momentum <p>.

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