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Assignments/Exercises
Assignment 1
- due Tuesday, February 18, 11:05 am
You may notice that this is the same as assignment 1 from 2019. Use
the solutions from 2019 at your peril.
Notes:
We gave a plan for the course and then reviewed some material on
multi-particle states of bosons
and fermions, considering both the spin and the spatial parts of their
wave functions. We also briefly reviewed the quantum mechanics of the
harmonic
oscillator and the hydrogen atom. We then made a small foray into atomic
physics and introduced the Aufbau Principle and Hund's
rules, which are
important in chemistry (construction of the periodic table relates to the
Aufbau principle) and also for remembering the magnetic
properties of the ground states of atoms and some ions. The spin,
orbital and total angular momentum of the electrons in an atom can be
determined using
Hund's rules and the information is summarized in the so called term
symbol of the atom.
Week 2
Notes:
We dealt with multi-particle states for bosons and fermions in some
detail. In particular we introduced full symmetrization and
antisymmetrization of products of single particle wave functions.
Antisymmetrization involved the signature (or sign) of a permutation or
the epsilon-symbol, if one prefers. It also led to wave functions
which are so called Slater determinants. We then introduced
Fock space, the vacuum state and creation and annihilation operators. For
fermions we showed the definition of the operators explicitly as well as
the canonical anticommutation relations (we also introduced the
anticommutator).
Week 3
Notes:
We will complete the introduction to creation and annihilation operators
(in particular give the canonincal commutation relations for the bosonic
operators). We then discuss how to write Hamiltonians for
interacting particles in terms of these operators. hopefully we will be
able to consider some example systems, such as the interacting electron
gas described by the so called "jellium model".