# Quantum Physics Help

1. Feb 5, 2010

### andyfreesty1e

Quantum Physics Help!!

1. The problem statement, all variables and given/known data
The spring constant for a particle in the ground state of a simple harmonic oscillator changes by a factor a^4 instantaneously, what is the probability that the particle is observed in the ground state of the new potential immediately following the change

can anyone give me a step in the right direction please, i think i have to use perturbation theory, but havent really been taught how to

2. Relevant equations
v(x)=(a^4)(kx^2)/2 is the new potential

3. The attempt at a solution

2. Feb 5, 2010

### gabbagabbahey

Re: Quantum Physics Help!!

There's no need for perturbation theory here. Just ask yourself two questions:

(1)What is the ground state of the harmonic oscillator both before and after the change in spring constant?

(2)If I'm told that a particle is in the state $|\psi_1\rangle$ and I want to find the probability that it is measured in the state $|\psi_2\rangle$, what equation would I use?

The answer to number (1) is derived in most introductory QM texts, and the answer to number (2) is often taken to be one of the postulates of QM.

3. Feb 6, 2010

### andyfreesty1e

Re: Quantum Physics Help!!

so the ground state before is (1/a(sqrt Pi))^1/2 exp[-x^2/2a^2] where a=(h_bar/mw)^1/2
and w=(k/m)^1/2 so the ground state after is the same but w=(a^4k/m)^1/2 ?

so then calculate c=integral (psi*Psi(x,0))dx
and then c^2 is the probability?

4. Feb 6, 2010

### gabbagabbahey

Re: Quantum Physics Help!!