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Question
Suppose a particle of mass m and charge q is in a one-dimensional harmonic oscillator potential with natural frequency wo. For times t > 0 a time-dependent potential of the form V₁(x,t) = εx cos(wt) is turned on. Assume the system starts in an initial state In). 1. Find the transitionn probability from initial state (n) to a state \n') with n' ‡ n. 2. Find the transition rate (probability per unit time) for the transition (n) → \n'). Note: (n'|x|n)= = ħ 2mwo (√√n +18n',n+1 + √ñdn',n−1).
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Transcribed Image Text:Suppose a particle of mass m and charge q is in a one-dimensional harmonic oscillator potential with natural frequency wo. For times t > 0 a time-dependent potential of the form V₁(x,t) = εx cos(wt) is turned on. Assume the system starts in an initial state In). 1. Find the transitionn probability from initial state (n) to a state \n') with n' ‡ n. 2. Find the transition rate (probability per unit time) for the transition (n) → \n'). Note: (n'|x|n)= = ħ 2mwo (√√n +18n',n+1 + √ñdn',n−1).
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