Quantum Mechanics for Mathematicians: The
Rotation and Spin Groups in 3 and 4 Dimensions
Peter Woit
Department of Mathematics, Columbia University
[email protected]
October 25, 2012
Among the bas
Quantum Mechanics for Mathematicians:
Problem Set 6
Due Wednesday, December 12
Problem 1: Fill in the details of the proof of the Groenewold-van Hove theorem
following the outline given in Chapter 5.4
Quantum Mechanics for Mathematicians: The
group U (1) and Charge
Peter Woit
Department of Mathematics, Columbia University
[email protected]
September 17, 2012
In classical electrodynamics, the s
Quantum Mechanics for Mathematicians:
Problem Set 5
Due Wednesday, November 29
Problem 1: Consider the action of SU (2) on the tensor product V 1 V 1 of two
spin one-half representations. According to
Quantum Mechanics for Mathematicians:
Problem Set 4
Due Wednesday, November 7
Problem 1: Using the denition
< f, g >=
1
2
2
f (z1 , z2 )g (z1 , z2 )e(|z1 |2+|z2 | ) dx1 dy1 dx2 dy2
C2
for an inner pro
Quantum Mechanics for Mathematicians:
Problem Set 2
Due Monday, October 8
Problem 1: Calculate the exponential etM for
0
0
0
0
0
0
0
by two dierent methods:
Diagonalize the matrix M (i.e. write as P
Quantum Mechanics for Mathematicians:
Problem Set 3
Due Monday, October 22
Problem 1: On the Lie algebras g = su(2) and g = so(3) one can dene the
Killing form K (, ) by
(X, Y ) g g K (X, Y ) = tr(XY
Quantum Mechanics for Mathematicians:
Two-state systems and spin 1/2
Peter Woit
Department of Mathematics, Columbia University
[email protected]
October 9, 2012
The simplest truly non-trivial qua
Quantum Mechanics for Mathematicians: Linear
Algebra Review, Unitary and Orthogonal Groups
Peter Woit
Department of Mathematics, Columbia University
[email protected]
September 24, 2012
A course
Quantum Mechanics for Mathematicians:
Representations of SU (2) and SO(3)
Peter Woit
Department of Mathematics, Columbia University
[email protected]
December 5, 2012
The group SO(3) acts by rota
Quantum Mechanics for Mathematicians: Tensor
Products, Entanglement, and Addition of Spin
Peter Woit
Department of Mathematics, Columbia University
[email protected]
November 15, 2012
If one has
Quantum Mechanics for Mathematicians:
Introduction and Overview
Peter Woit
Department of Mathematics, Columbia University
[email protected]
September 24, 2012
1
Introduction
A famous quote from R
Quantum Mechanics for Mathematicians: The
Spin 1 Particle in a Magnetic Field
2
Peter Woit
Department of Mathematics, Columbia University
[email protected]
October 15, 2012
The existence of a non
Quantum Mechanics for Mathematicians: Lie
Algebras and Lie Algebra Representations
Peter Woit
Department of Mathematics, Columbia University
[email protected]
October 1, 2012
For a group G we hav
Quantum Mechanics for Mathematicians:
Problem Set 1
Due Monday, September 24
Problem 1:
Consider the group S3 of permutations of 3 objects. This group acts on the
set of 3 elements. Consider the repre