Physics 745 - Group Theory
Solution Set 23
1. [20] The group SU(2) shows up in surprising places. Consider, for example, the
two-dimensional harmonic oscillators, which can be written in the form
H =
Physics 745 - Group Theory
Solution Set 27
1. [5] This problem has to do with demonstrating that according the isospin
symmetry, the three s all have the same mass.
(a) [2] Work out the effects of the
Physics 745 - Group Theory
Solution Set 28
1. [15] The group SU(3) contains the group SU(2) as a subgroup, and in more than
one way
(a) [7] Show that the generators T1, T2 and T3 form an SU(2) subgrou
Physics 745 - Group Theory
Solution Set 29
1. [5] Using a weight diagram, or tensor methods (your
choice), work out the decomposition of the tensor product
3 3 into irreps.
T8
If you add the three wei
Physics 745 - Group Theory
Solution Set 30
1. [5] The mass of the can be predicted in terms of the parameters a and b from
eq. (4.36).
(a) [2] Find the formula for the mass in terms of a and b.
This i
Physics 745 - Group Theory
Solution Set 25
1. [15] In the electric dipole approximation, the rate at which an atom decaying
from one state to another by the emission of a photon is given by
2
3
( I F
Physics 745 - Group Theory
Solution Set 24
1. [5] The total angular momentum of an atom actually has three pieces: The
orbital angular momentum of the atom, the spin of the electron, and the spin of
t
Physics 745 - Group Theory
Solution Set 20
1. [10] Prove, using only the commutation relations, the first three identities (2.9)
from the notes, namely
T2 , Ta = 0,
[T3 , T ] = T ,
and T2 = TT + T32
Physics 745 - Group Theory
Solution Set 21
1. [10] In class (or the notes), I gave explicit instructions for how to find the
j
irreducible representations Ta( ) . To demonstrate that you understand th
Physics 745 - Group Theory
Solution Set 22
1. [10] It is rare we will actually use the representation matrices ( j ) ( R ) , but
occasionally it is useful. We want to work out explicitly ( 2 ) ( R ( x
Physics 745 - Group Theory
Solution Set 26
1. [10] Below is a list of reactions that are possible. You should know the charge
and baryon number of the proton (p), electron (e) and
neutron (n). Deduce