Quiz: a quiz is now posted here.

 A quiz is posted here. I think it might take a couple hours even if you are well prepared. In preparation for this quiz I would suggest the you review:
the ground state and 1st excited states of the hydrogen atom (r, x, y, z form),
the first 3 eigenstates of the 1DHO and their energies,
how time dependence works in quantum mechanics,
how to calculate expectation values, and
how and why some expectation values are time dependent and others are not.
Also, I would suggest preparing a table with integrals such as: (see image to the left)

and also similar integrals with x^2, x^4, x^6, x^8, as well as x^0 (constant) multiplying the exponential in the integrand. (This sort of integral tends to come from the product of two HO eigenstates, right?) Also include values of things like $\hbar c$, $mc^2$ (for an electron). Finally I would recommend studying graphing, graphing and graphing (including contour plots).  I'll post the quiz later this weekend. I wanted to give you time to prepare before you see it. I believe that the more you prepare for this just like an in-class quiz or midterm, and the more you do it right away once you see it, and time yourself and use only a note sheet prepared in advance of looking at the quiz... The more you do those sorts of things, the more it will help you prepare for the in-class midterm and final.
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Quiz 1.
1. Graph $e^{-r/a}$ as a function of x along the x-axis.
    What is its value at x=0, y=0 and z=0?
    What is its value at x=a, y=0 and z=0?

2. Graph $(x/a)e^{-r/2a}$ as a function of x along the x-axis.
    What is its value at x=0, y=0 and z=0?
    What is its value at x=2a, y=0 and z=0?

3. Evaluate $\hbar^2/(ma^2)$ in units of eV.  m refers to the mass of an electron and a=0.05 nm. (You do not have to be very precise here. Just do a reasonable calculation that shows that you are prepared to do this sort of evaluation.)

4. Do a contour plot in the y-z plane illustrating the nature of the quantum state $(4 \pi a^3)^{-1/2} e^{-r/2a}(z/2a)$.

5. Suppose that at t=0 the wave-function of an electron in a 1D harmonic oscillator is:
$\psi(x) = (\psi_o (x) + \psi_2 (x))/\sqrt{2}$.
a) Calculate $\bar{x^2}$.
b) Is $\bar{x^2}$ a function of time? why or why not?
c) How is $\bar{x^2}$ related to the potential energy?

6. Write a paragraph, or several paragraphs, in which you:
    include in the beginning a graph of $\bar{x^2}$ as a function of time for an electron in the state from problem 5, and discuss the relationships between $\bar{x^2}$, potential energy and kinetic energy in the context of that graph.  Include also sketches of wave-functions at different times illustrating how confinement varies with time for this state and discuss how that relates to KE and PE.