Modern 2:Overview of Chapter 3
(Difference between revisions)
| Line 15: | Line 15: | ||
Here is a fundamental result '''which you should prove''': | Here is a fundamental result '''which you should prove''': | ||
| − | <math> \langle \vec{p} _x \rangle _ t = -i \hbar \int \psi^*(\vec{r},t) \partial _x \psi(\vec{r},t) d^3 r </math> | + | <math> \langle \vec{p} _x \rangle _ t = -i \hbar \int \psi^*(\vec{r},t) \partial _x \psi(\vec{r},t) d^3 r </math> '''(3.4)''' |
<math> \partial _x </math> means partial with respect to <math>x</math>. | <math> \partial _x </math> means partial with respect to <math>x</math>. | ||
The vector form of | The vector form of | ||
Revision as of 00:21, 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:
(3.4)
means partial with respect to x.
The vector form of
