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

## 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) 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) 21/4/(1+ 21/2)
(B) 25/4/(1+21/2)
(C) 2/(1+21/2)
(D) 23/2/(1+21/2)

## 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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vela
Staff Emeritus
Homework Helper
Your expression for the ground-state wave function has errors as the argument of the exponential isn't unitless.

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

I am attaching my solution in the attachment below.

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vela
Staff Emeritus