Modern 2:More on Square Wells and Review for Monday's Exam
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to each physical quantity <math>A</math> there is an associated observable | to each physical quantity <math>A</math> there is an associated observable | ||
given as a self-adjoint operator <math>\hat{A}</math>. And that | given as a self-adjoint operator <math>\hat{A}</math>. And that | ||
| − | the expected value of a measurement associated with this quantity is given by <math>\langle | + | the expected value of a measurement associated with this quantity is given by <math>\langle \psi |
|\hat{A}|\psi \rangle = \int \psi^*(\mathbf{r},t) \left[ \hat{A} \psi(\mathbf{r},t) \right] d^3 r</math>. | |\hat{A}|\psi \rangle = \int \psi^*(\mathbf{r},t) \left[ \hat{A} \psi(\mathbf{r},t) \right] d^3 r</math>. | ||
Revision as of 16:02, 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.
- und
