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AegisAndAtrophy
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Homework Statement
At t<0 a particle is in the ground state of the potential V(x)= [tex] \frac{1}{2} mw^2x^2 [/tex]. At t=0 the potential is suddenly displaced by an amount x0 to V(x)= [tex] \frac{1}{2} mw^2(x-x_0)^2 [/tex] .
a) What is the probability of the particle being in the ground state; the first excited state?
b) At t=[tex] \frac{2pi}{w} [/tex] write the wave function
Homework Equations
The Attempt at a Solution
I think that the wave function should be [tex] Ψ_0(x,0)= (\frac{mw}{πh})^\frac{1}{4} e^ \frac{-mw(x-x_0)^2}{2h} [/tex]
I'm not sure what I should do though in order to find the probability in the ground state.
For the first excited energy I know I need to use the raising operator in order to get the wave function, which would give me [tex] (\frac{mw}{h})^\frac{1}{2} [/tex] times [tex] Ψ_0 [/tex] but again I'm unsure how to find the probability.