Modern 2:More on Square Wells and Review for Monday's Exam
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* if the wavefunction IS an eigenfunction of some observable <math>\hat{A}</math> with eigenvalue <math>a</math>, the the measurement of <math>A</math> is equal to <math>a</math> with probability 1. | * if the wavefunction IS an eigenfunction of some observable <math>\hat{A}</math> with eigenvalue <math>a</math>, the the measurement of <math>A</math> is equal to <math>a</math> with probability 1. | ||
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+ | There are two potential problems that will be fair game for Monday's exam. First is the finite step potential: | ||
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+ | <math>V(x) = V_0 \hbox{if } 0 \leq x \leq a <math> and zero otherwise</math> |
Revision as of 16:12, 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 .
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.
- the eigenstates are orthogonal and complete. This lets us represent any wavefunction as a superposition of eigenstates.
- if the wavefunction IS an eigenfunction of some observable with eigenvalue a, the the measurement of A is equal to a with probability 1.
There are two potential problems that will be fair game for Monday's exam. First is the finite step potential: