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

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It's a quantum mechanics question. help_outlineImage TranscriptioncloseA 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? fullscreen
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Step 1

Using the definition for probability from time-dependent perturbation theory, help_outlineImage Transcriptionclose)W» (i ) di Po(1) =[exp(i@ Here, Wa(t) =( \|W(})|)} -(4-*) = -Fe"* <끼지0〉 fullscreen
Step 2

In the operator notation, the position operator is,

Step 3

Using the expression for energy...

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