Modern 2:Overview of Chapter 3
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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> | ||
− | 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 these numbers refer the equation numbers in the book) |
<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 |
Revision as of 00:20, 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 these numbers refer the equation numbers in the book)
means partial with respect to x.
The vector form of