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The wavefunction for the particle in a one-dimensional infinite potential well is given by n2n?h? V(1,t) = NAL' e -iEnt/h En sin %3D 2mL2' with 0

The wavefunction for the particle in a one-dimensional infinite potential well is given by n2n?h? V(1,t) = NAL' e -iEnt/h En sin %3D 2mL2' with 0

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The wavefunction for the particle in a one-dimensional infinite potential well is given by V(x, t) = VI 2 e-iEnt/h En n?n?h? sin 2mL2 with 0<r<L and n = 1,2,3, . 1. Show that V (r, t) is normalized. 2. The uncertainty, Aq, in the measurement of an observable, q, is formally defined as Aq = Va) – (4)², where (·) is the expectation value as defined in the notes. Calculate the uncertainty in the measurement of the position and momentum of the particle in the box. That is, calculate Ar and Ap.
Transcribed Image Text:The wavefunction for the particle in a one-dimensional infinite potential well is given by V(x, t) = VI 2 e-iEnt/h En n?n?h? sin 2mL2 with 0<r<L and n = 1,2,3, . 1. Show that V (r, t) is normalized. 2. The uncertainty, Aq, in the measurement of an observable, q, is formally defined as Aq = Va) – (4)², where (·) is the expectation value as defined in the notes. Calculate the uncertainty in the measurement of the position and momentum of the particle in the box. That is, calculate Ar and Ap.
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