Modern 2:Overview of Chapter 3
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'''Reminder''' | '''Reminder''' | ||
− | <math> \langle r \rangle _ t </math> | + | <math> \langle r \rangle _ t = \int r |\psi(r,t)|^2 d^3 r </math> |
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+ | <math> \langle p \rangle _ t = \int p |\phi(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>L = r \times p</math> | ||
+ | |||
+ | Here is a fundamental result which you should prove: | ||
+ | <math> \langle p _x \rangle _ t = \int \psi^*(r,t) \partial _x \psi(r,t) d^3 r </math> |
Revision as of 00:09, 24 February 2006
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: