10
Self-consistent eld theory
An important unsolved problem in quantum mechanics is how to deal with indistinguishable, interacting particles - in particular electrons which determine the behaviour of almost every object
in nature. The basic problem is th
9
Indistinguishable Particles and Exchange
Quantum mechanics allows us to predict the results of experiments. If we conduct an experiment
with indistinguishable particles a correct quantum description cannot allow anything which distinguishes between them
8
8.1
The Variational Principle
Approximate solution of the Schroedinger equation
If we cant nd an analytic solution to the Schroedinger equation, a trick known as the variational principle allows us to estimate the energy of the ground state of a system.
7
+
The H2 Ion and Bonding
As the simplest example of covalent bonding, we consider the hydrogen molecular ion.
electron
+
The hydrogen molecular ion H2 is a system composed of
two protons and a single electron. It is useful to use centre
of mass (cm) coo
5.6
Example of Golden rule - beta decay
A nucleus decays via the reaction n p e . to form a electron and antineutrino, releasing
energy E0 .
The simplest form for the matrix element describing nuclear -decay is given by the so-called Fermi
ansatz Vmk = GF
5
5.1
Timedependence
Timedependent Hamiltonians
Recall that for a system described by a Hamiltonian, H0 , which is timeindependent, the most
general state of the system can be described by a wavefunction |, t which can be expanded in
the energy eigenbasis
4
4.1
Degeneracy, Symmetry and Conservation Laws
Distinguishing between eigenstates, Quantum numbers as labels
How can we distinguish between quantum states |n which have degenerate values of A? The
obvious way is to measure the quantised observables and
3
3.1
Dealing with Degeneracy
Time-Independent Degenerate Perturbation Theory
We have seen how we can nd approximate solutions for a system whose Hamiltonian is of the
form
H = H0 + V
When we assumed that H and H0 possess discrete, non-degenerate eigenval
2
Review: Time-Independent Non-degenerate Perturbation Theory
Theres nothing new in this section, its simply an alternative derivation to the one you saw last
year in Junior Honours. If you prefered that derivation, feel free to read over those notes, the
1
Summary of things you should already know
I think I can safely say that nobody understands quantum mechanics Richard Feynman
1.0
Prerequisite
All material covered in Junior Honours Quantum Mechanics is part of the syllabus of this course.
1.1
Understand