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What sections is the quiz covering again?
I believe it is just up to and including section 2.3.
When using eq. 2.67 from the book, how exactly does the (a+)^n portion of the equation work? If I wanted to find <math>\psi_2(x)</math>, do I have to first square the a+ operator, or can I find <math>\psi_1(x)</math> and apply the operator again? Or does it not matter at all?
You can find <math>\psi_1</math> first and go from there. You'll just have to keep track of the <math>\frac{1}{\sqrt{n}}</math> terms.
you can do it both ways. you can operate on <math>\psi_0</math> once and get <math>\psi_1</math> and operate on <math>\psi_1</math> to get <math>\psi_2</math> or you can use (a+)^2 (which expands to give you 4 terms) and operate on <math>\psi_0</math>.
Back for another question. How do we find the probability of getting a specific energy (last problem of the practice quiz)?
The probability of finding the particle to have the energy corresponding to a specific state is <math>C_n^2</math>.
Where is the square root of one comes from when calculating <x> in problem 2.13 in the solution?