Modern 2:More on Square Wells and Review for Monday's Exam
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In addition to this summary, you should understand | In addition to this summary, you should understand | ||
| − | # the ininite square well sufficiently to be able to derive the energy eigenstates, | + | # the ininite square well sufficiently to be able to derive the energy eigenstates, the energy levels and normalization. |
| − | the energy levels and normalization. | + | |
| − | # | + | # the eigenstates are orthogonal and complete. This lets us represent any wavefunction as a superposition of eigenstates. |
| + | |||
| + | # if the wavefunction IS an eigenfunction of some observable <math>\hat{A}</math> with eigenvalue | ||
| + | <math>a</math>, the the measurement of <math>A</math> is equal to <math>a</math> with probability 1. | ||
Revision as of 16:07, 10 March 2006
There is a review of important topics at the end of chapter 3, pages 58-59. I will go over this
in class today. But briefly, it includes the time dependent and time independent Schrodinger equations.
Momentum space representation. The Heisenberg uncertainty relation (for x, p_x and E, t). The idea that
to each physical quantity A there is an associated observable
given as a self-adjoint operator 
. And that
the expected value of a measurement associated with this quantity is given by ![\langle \psi
|\hat{A}|\psi \rangle = \int \psi^*(\mathbf{r},t) \left[ \hat{A} \psi(\mathbf{r},t) \right] d^3 r](/csm/wiki/images/math/c/1/2/c1247c7e65273b11e9d6e16a338c18bd.png)
.
In addition to this summary, you should understand
- the ininite square well sufficiently to be able to derive the energy eigenstates, the energy levels and normalization.
- the eigenstates are orthogonal and complete. This lets us represent any wavefunction as a superposition of eigenstates.
- if the wavefunction IS an eigenfunction of some observable with eigenvalue
a, the the measurement of A is equal to a with probability 1.
