- #1
Denver Dang
- 148
- 1
Homework Statement
Hi... My problem says:
In a given experiment the system, at the time [itex]t = 0[/itex], in the normalized state is given by:
[tex]\phi(t =0) = \frac{1}{\sqrt{5}}(i\psi_{210} + 2\psi_{211})[/tex]
What possible outcomes is possible if you do an energy measurement on the system in this state, and with what probability does this occur ?
Homework Equations
I know that the states [itex]\psi_{21-1}, \psi_{210}[/itex] and [itex]\psi_{211}[/itex] is given by the matrix [itex]H[/itex]:
[tex]\[ \left( \begin{array}{ccc}
E_{2} + 2\gamma\hbar^{2} & 0 & 0 \\
0 & E_{2} + 2\gamma\hbar^{2} & 0 \\
0 & 0 & E_{2}\end{array} \right)\][/tex]
Don't know if I need to be telling more ?
The Attempt at a Solution
Well, I know the outcome has to be the two last states (In the order I wrote my states), which means: [itex]\psi_{210}[/itex] and [itex]\psi_{211}[/itex].
This means that I have to calculate the probability for those two, which means: [itex]P(E_{2} + 2\gamma\hbar^{2})[/itex] and [itex]P(E_{2})[/itex].
My problem is, that I'm not quite sure how to calculate that :/
My book says:
[tex]P(j) = \frac{N(j)}{N},[/tex]
but I have no idea how to make use of that in this case.
I know the answer should be: [itex]P(E_{2} + 2\gamma\hbar^{2}) = \frac{1}{5}[/itex] and [itex]P(E_{2}) = \frac{4}{5},[/itex]
but again, not sure how to do it.
So I was hoping someone could give me some pointers towards this, probably, easy question :)
Regards.