Question
Asked Dec 4, 2019
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It's a quantum mechanics question.

A one-dimensional harmonic oscillator begins in its ground state at time t = 0. For t > 0, the
oscillator is subject to a time dependent force of
F(t) Foet/
(2)
Using time-dependent perturbation theory to first order, obtain the probabililty of finding the particle
in its first excited state for t > 0. Show that your result is independent of time as t > o0. Is this
surprising?
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A one-dimensional harmonic oscillator begins in its ground state at time t = 0. For t > 0, the oscillator is subject to a time dependent force of F(t) Foet/ (2) Using time-dependent perturbation theory to first order, obtain the probabililty of finding the particle in its first excited state for t > 0. Show that your result is independent of time as t > o0. Is this surprising?

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Expert Answer

Step 1

Using the definition for probability from time-dependent perturbation theory,

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)W» (i ) di Po(1) =[exp(i@ Here, Wa(t) =( \|W(})|)} -(4-*) = -Fe"* <끼지0〉

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Step 2

In the operator notation, the position operator is,

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2mo (ata')

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Step 3

Using the expression for energy...

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E„- E, (*+) ho-(0+}r® = no

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