|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
more comfortable with Hamilton's formulation of classical mechanics than many
of us are - students who got an A+ in PHY 521 last semester are in good shape!).
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 on 1st February. The list of topics has been updated
with links to individual student projects done mostly last year.
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:
Blackbody radiation, reasons for failure
of classical description in terms of equipartition of energy amongst normal modes
of a cavity: Planck hypothesis.
Compton effect, i.e. inelastic scattering of radiation
with momentum which is quantized.
The Inverse Compton effect is important in
current astrophysical models.
The Bohr atom, stability of orbits against
classical expectations, and the correspondence principle, showing that for large n
(and actually large l and m also) one should get the same result from both the Bohr and
the classical pictures. Yes, we know the Bohr picture is incorrect, and should be
consigned to history...
The uncertainty principle, and the qualitative reasons for not being able
to determine position and momentum simultaneously with arbitrary precision.
Differential equations, up to second order, and the difference between
ordinary and partial DE's, with examples of their solutions.
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.
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 and 3x3 matrices.