Modern 2:Overview of Chapter 3
(Difference between revisions)
| Line 10: | Line 10: | ||
<math> \langle \vec{r} \rangle _ t = \int \vec{r} \ |\psi(\vec{r},t)|^2 d^3 r</math> | <math> \langle \vec{r} \rangle _ t = \int \vec{r} \ |\psi(\vec{r},t)|^2 d^3 r</math> | ||
| − | <math> \langle \vec{p} \rangle _ t = \int \vec{p} | + | <math> \langle \vec{p} \rangle _ t = \int \vec{p} \ |\phi(\vec{p},t)|^2 d^3 p </math> |
But we can also compute the expectation of <math>p</math> in position space. This is essential if we want to be able to treat variables such as angular momentum, which involve both position and momentum: <math>\vec{L} = \vec{r} \times \vec{p}</math> | But we can also compute the expectation of <math>p</math> in position space. This is essential if we want to be able to treat variables such as angular momentum, which involve both position and momentum: <math>\vec{L} = \vec{r} \times \vec{p}</math> | ||
Revision as of 00:19, 24 February 2006
Overview of Chapter 3
2/24/06
- The state of a system is system is described by a wavefunction. ψ(r,t). The wavefunction evolves deterministically according to the Schrodinger equation. However, we give a probabilistic interpretation to the wave function that allows us to predict the measurement of a given physical quantity.
- On the other hand, if we perform an experiment, the system will be in some state. How do we obtain as much information about this state.
- Finally, we may wish to perform an experiment on a system in a given state; i.e., one that is prepared experimentally to have well-defined properties.
Reminder
But we can also compute the expectation of p in position space. This is essential if we want to be able to treat variables such as angular momentum, which involve both position and momentum: 
Here is a fundamental result which you should prove:
means partial with respect to x.
