Physics 125a
Problem Set 2, Due Wed. Oct. 14, 2015
Problem 1
|K 0 and |K 0 are two orthogonal states with unit norm that correspond to the particles K 0 and K 0 . These
particles decay into other particles so if we approximate their physics as a two state
Physics 125a
Problem Set 4, Due Wed. Nov. 11, 2015
Problem 1
Using X =
that
2m (a + a ) and P =
X = n|X|n =
2m
m
i
(a
2
a), along with a|n =
n|(a + a )|n =
2m
n|n 1 , a |n =
n n|n 1 +
n + 1 n|n + 1
n + 1|n + 1 , we see
= 0,
(1)
By orthogonality of |n st
Physics 125a Midterm Solutions Due November 4, 2015
Problem 1
A quantum mechanical observable is represented by the Hermitian operator O. It has an orthonormal basis of eigenstates | , where O| = | . Suppose a system is prepared in a state
| =
|1 + | 1 +
Lecture 15. Canonical Transformations
(Dated: November 17, 2015.)
I.
REVIEW FROM LAST TIME AND SUMMARY OF THIS LECTURE
Last time, we discussed:
1. Examples of converting the Lagrangian into Hamiltonian dynamics.
2. Liouvilles Theorem: Phase Space Volume i
Ph125: Problem Set 5 Solutions
Chia-Hsien Shen
November 21, 2015
Problem 1
(a) The system is in the ground state of old SHO. The ground state is annihilated by its annihilation operator a,
a|0old = 0.
(1)
However, it is not true if we replace a by the new
Physics 125a
Problem Set 3, Due Wed. Oct. 21, 2015
Problem 1
We are given the Hamiltonian H = g = g1 1 + g2 2 + g3 3 . The basis vectors of the Hilbert Space are |1 and
|2 which are eigenstates of 3 with eigenvalues +1 and 1 respectively.
(a) We seek all
Physics 125a
Problem Set 6, Due Wed. Nov 25, 2015
Problem 1
(a) Two identical bosons are found to be in the states | and . Write
down the normalized state vector describing the system when | =
0.
(b) A particle moves in a potential V (x) = V0 sin(2x/a). T