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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?

Here is a study tip that I think might help with QM and I leave this tip up to discussion towards refinement. – Think of QM laterally in terms of big-concepts and sub-concepts. For example, delineate between the Time-Independent Schrodinger equation (big-concept) and separable solutions (sub-concept). The next part of the study tip is to think about the “How” and the “Why”. It's good to know how to solve separable solutions but it may be more important to know “Why” to use them. Focusing on the How and the Why of sub-concepts may make understanding the How and Why of big-concepts easier. This is my thought anyways. What do you think???

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