Fundamental physics, year 1
(Teknisk fysik, årskurs 4)
Advanced quantum mechanics — Lecture notes
Ferretti, Stellan Östlund and
The course home page can be found at
- Tuesday 2008-10-28
- New lecturer: Gabriele Ferretti.
Scattering. Cross section σ. Flux. Event. Differential cross
section. The Lippmann-Schwinger equation. Scattering from potential
↔ elastic scattering of two particles. Perturbation theory in a
continuum. Lippmann-Schwinger in the coordinate representation. The
- Wednesday 2008-10-29
- More on the Lippmann-Schwinger equation. What goes wrong if we
choose -iε in the denominator. Incoming and outgoing radial
waves. The current associated with a wave function. The scattering
amplitude f(p, p'). The relation
between scattering amplitude and differential cross section. The
first order Born approximation. Going from the centre of mass system
to the laboratory frame (hmm, we did not seem to finish that).
- Friday 2008-10-31
- I did not take notes this day. Sorry. I had to visit the
- Tuesday 2008-11-04
- The eikonal approximation. Partial waves.
- Wednesday 2008-11-05
- Partial waves. Partial wave scattering amplitude. Argand
diagrams. Connection eikonal — partial wave. Hard sphere
s-wave scattering. Analytic properties of the S
- Friday 2008-11-07
- Scattering with identical particles. Parity and time
reversal. The detailed balance. Inelastic scattering. The size of a
nucleus. Nuclear form factor. The Hilbert space, creation and
annihilation in quantum field theory.
- Tuesday 2008-11-11
- We only
take home exam. In problem two, averaging over the direction
of the incoming beam is good.
- Wednesday 2008-11-12
- New lecturer: Stellan Östlund. Multi-particle
systems. Kets with angle brackets and with round
parenthesis. Occupation number of the states. ξ = 1 for
bosons, ξ = -1 for fermions. Distinguishable and
indistinguishable particles. The Slater determinant. For bosons: the
permanent. The particle number representation. The
Fock-space. Creation and annihilation operators.
- Friday 2008-11-14
- Bosons and fermions: commutation and anti-commutation
relations. Matrix representation of creation operators. Unitary
transformation. Commutation with the number operator. The
Hamiltonian. Second quantisation. Normal ordered.
- Tuesday 2008-11-18
- Canonical transformations for fermions and
bosons. Bogoliubov-Valatin transformation. Weakly interacting Bose
gas. For the theory of the weakly interacting Bose gas, we use
e-book via Chalmers library.
- Wednesday 2008-11-19
- Weakly interacting Bose gas. Non-interacting ground state not
eigenstate of interacting Hamiltonian. The number of particles is
not necessarily a good quantum number. Creation and annihilation
operators approximated as c-numbers. Hartree term. Fock
term (exchange term). Anomalous term. Bug in superfluid.
- Friday 2008-11-21
- The difficulty in handling lots of particles. Landau-Ginzburg
theory. Global phase transformation is a symmetry: Goldstone's
theorem. What we mean by momentum. Wick's theorem.
- Tuesday 2008-11-25
- Wednesday 2008-11-26
- Friday 2008-11-28
- Not too much here, the interesting stuff are on
slides used in this lecture.
- Tuesday 2008-12-02
- New lecturer: Bernhard Mehlig. Bohr's model of
the hydrogen atom. De Broglie waves and classical paths. Pauli's
Ph.D. thesis [from the description, I'm guessing it
one]. The Schrödinger equation for a free particle: Hamilton's
principal function. The correspondence principle. The group
velocity is the classical velocity. The connection between the
time-independent wave-function and the Maupertuis action. The
Maupertuis principle δS=0. Fermat's principle. Classical
mechanics: Lagrangian mechanics. Lagrange function. Variational
principle and Lagrange's equations. Hamiltonian mechanics and
Hamilton's equations. The Hamilton-Jacobi equation.
- Wednesday 2008-12-03
- A particle bound in a potential. Writing the Schrödinger
equation in terms of the classical momentum p(x) instead of
energy and potential V(x). Expanding the action S(x)
in powers of ħ. The WKB wave function. Borel-resummation.
The harmonic oscillator in the WKB approximation. Turning
points. Patching with a linearised potential. The exact solution of
the linearised problem.
- Friday 2008-12-05
- The stationary phase approximation. Fresnel integrals. Patching
with the Airy function. Matching the wave-functions in the
middle. Path integrals in phase space. The WKB quantisation
condition. Maslov index. Turning points. Caustics.
- Tuesday 2008-12-09
- WKB quantisation. Quantizing the Harmonic oscillator. The Maslov
index. Area in phase space. In several dimensions: Action-angle
coordinates. Tori in phase space. Scattering. ...
- Wednesday 2008-12-10
- Scattering. ...
- Friday 2008-12-12
- Adiabatic theorem. Berry's phase. ...
Christian von Schultz <email@example.com>