Physics 751: Final Study Guide 2008
Review all the answers to homework problem sets and read your own notes from class.
I will ask no questions on the historical stuff at the beginning,
except for the purely physics content
.
For
example, you should have a good understanding of the Bohr atom, including the classical limit of a very
large atom and how that fixes the quantum of angular momentum, and know how the Uncertainty
Principle can be used to estimate the size of bound states, such as the atom on the table.
You should know Schrödinger’s equation by heart, the probability interpretation of the wavefunction,
the conservation of probability current, and the expectation value of an operator.
Be able to find the time
‐
dependent probability and current distribution for a superposition of states of
different energies.
Know the definition of the delta function as a limit of a Gaussian wavepacket, and be able to Fourier
transform a Gaussian wavepacket. (Know the integral you need by heart.)
Also, know how to do
Fourier series and transforms for simple functions, and be able to discuss the limitations of Fourier
series for
discontinuous
functions.
You must know the bra and ket notation, be able to construct the first few elements of an orthogonal
basis, the definitions of adjoint, Hermitian and unitary, and be able to diagonalize a Hermitian or a
unitary matrix. Know the definition of determinant and trace, and how these relate to eigenvalues.
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 Fall '07
 MichaelFowler
 Angular Momentum, Work, Uncertainty Principle

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