A particle of mass 'm' is initially in a ground state of 1- D Harmonic oscillator potential V(x)....

[Sushmita]

Homework Statement

[/B]
A particle of mass 'm' is initially in a ground state of 1- D Harmonic oscillator potential V(x) = (1/2) kx² . 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 dimensional 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

 

[vela]

Your expression for the ground-state wave function has errors as the argument of the exponential isn't unitless.

Your approach is fine, but we can't really help you if you don't show your calculations.

 

[Sushmita]

Your expression for the ground-state wave function has errors as the argument of the exponential isn't unitless.

Your approach is fine, but we can't really help you if you don't show your calculations.

I am attaching my solution in the attachment below.

 

[vela]

To calculate an inner product, you need to evaluate an integral.