(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 ?

2. Relevant 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 ?

3. 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.

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# Homework Help: Finding the probability of energy measurements

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