# Homework Help: Probability of finding a system an eigenstate

1. Aug 31, 2014

### krobben92

1. The problem statement, all variables and given/known data

As the homework problem is written exactly:
Consider the quantum mechanical system with only two stationary states |1> and |2> and energies E0 and 3E0, respectively. At t=0, the system is in the ground state and a constant perturbation <1|V|2>=<2|V|1>=E0 is switched on. Calculate the probability of finding the system in the state |2>.

2. Relevant equations
H=V (I'm just assuming these states must be such that there is no kinetic energy and E=V, but that's just my guess - professor lacks communication skills at times).

|c1|2 + |c2|2 = 1
P(|2>)=|c2|2 (thus, I need c2 to solve the problem!)

3. The attempt at a solution
Well, I'm completely confused as to why he gave us <1|V|2>=<2|V|1>=E0, what that even means, and where I'm supposed to retrieve the probability coefficients which is all I need to solve the problem.

2. Sep 1, 2014

### nrqed

Hi there!

Have you learned non degenerate perturbation theory? This is the formalism required to do this problem. What formula have you seen for perturbation theory?

3. Sep 1, 2014

### krobben92

No, at least not that I know of. I'm familiar with chapters 1-4 in Griffiths, if that helps.

4. Sep 1, 2014

### vanhees71

Also you are given the complete information about the unperturbed Hamiltonian!

5. Sep 1, 2014

### krobben92

Right, I get that I have all of the matrix elements of the Hamiltonian, but I'm not sure how that's going to help me determine that probability of finding the system in state |2>. Also, we've never covered non degenerate perturbation theory, so is there another more elementary way to solve this problem?

6. Sep 1, 2014

### vela

Staff Emeritus
No, this isn't right. You add V to the existing Hamiltonian, so H=H0+V. What are the matrix representations of H0, V, and H? You should be able to figure out the rest from there.