8.513 Problem Set 5
(Dated: October 15, 2004)
Due Oct 28
1. Consider a system of bosons interacting with each other through some generic twobody interaction V (r). In
this problem you will study various aspects of the superuid state in some generality.
8.513 Problem Set 4
(Dated: October 5, 2004)
Due Oct 12
1. Calculate the temperature dependence of the specic heat of a three dimensional superuid at low temperature.
Assume that the sound wave velocity is some number c.
2. Melting curve of He4 at low tem
8.513 Problem Set 3
(Dated: September 29, 2004)
Due Oct 5
1. Consider a particle of mass m moving in a potential V (x) = k x2 + ux4 with u > 0.
(a) Rewrite the Hamiltonian in terms of creation and annihilation operators.
(b) Write the quantum partition fu
8.513 Problem Set 2
(Dated: September 21, 2004)
Due Sept 28
1. Consider the imaginary time propagator K (x, y ; ) =< x|eH |y > for a quantum system with Hamiltonian H .
(a) Show that for large , K (x, y ; ) 0 (y )0 (x)eE0 where 0 (x) is the ground state w
8.513 Problem Set 1
(Dated: September 15, 2004)
Due Sept 21
Practice with creation / annihilation operators
1. Consider a situation where an electron can hop between two dierent localized regions of space (eg: the vicinity
of each nucleus in a diatomic mo