| Background information for quantum physics is contained in many books,
particularly in the first few chapters. If you are using Gasiorowicz, then
you can treat the first two chapters as background which should be understood,
if not in advance, then as the course proceeds. If you are using Liboff, the
same material is covered in chapter 2. (I will not use his chapter 1 explicitly,
but it is interesting to remember that the founders of quantum mechanics were
much more comfortable with Hamilton's formulation of classical mechanics
than we are - in general, that is!). Some of the examples discussed
are taken from the earlier book by Dicke and Wittke.
I will start the course by checking whether you feel comfortable with
the following material, and will incorporate a selection of it into the
diagnostic test, to be taken at a time we agree on, provisionally scheduled for 30th
January.
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Blackbody radiation, reasons for failure of classical description in terms
of equipartition of energy amongst normal modes of a cavity: Planck hypothesis.
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Compton effect, i.e. inelastic scattering of radiation with momentum which is quantized.
The Inverse Compton effect is important in current
astrophysical models.
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Bohr atom, stability of orbits against classical expectations, and the
correspondence principle, showing that for large n one should get the same
result from both the Bohr and the classical pictures. Yes, we know the
Bohr picture is incorrect...
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The uncertainty principle, and the qualitative reasons for not being able
to determine position and momentum simultaneously with arbitrary precision.
Related to these physical effects, there are mathematical tools, which
will be introduced as we need them through the course. However, it will
be helpful if you are clear about the following:
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Differential equations, up to second order, and the difference between
ordinary and partial DE's, with examples of their solutions.
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Fourier series, transforms and integrals. There
is a website where you can
amuse yourself with integrals, and we might usefully make some lists of
integrals we need as the course proceeds.
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Linear algebra and matrices. Be sure you remember
how to construct matrices and can find the characteristic roots, or
eigenvalues and eigenvectors in simple cases, starting with 2x2 matrices.
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