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Homework Statement
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A particle of mass 'm' is initially in a ground state of 1 D Harmonic oscillator potential V(x) = (1/2) kx^{2} . If the spring constant of the oscillator is suddenly doubled, then the probability of finding the particle in ground state of new potential will be?
(A) 2^{1/4}/(1+ 2^{1/2})
(B) 2^{5/4}/(1+2^{1/2})
(C) 2/(1+2^{1/2})
(D) 2^{3/2}/(1+2^{1/2})
Homework Equations
I calculated state with the wave function of one dimentional harmonic oscillator given by
Ψ = (k/πħ)^{¼} exp ^{(kx2/2ħ)}
When k was doubled, new wave function becomes
Ψ'= (2k/πħ)^{¼} exp ^{(2kx2/2ħ)}
The Attempt at a Solution
I tried solving the question by calculating the probability by finding the inner product of the two but I cannot solve it
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