PHY 215A, Quantum Mechanics: Solutions to Homework Set #1
1. Vector Spaces.
Because our definition of multiplication and addition match the regular definitions, we only need to check
closure and show that |0 > exists as well as an inverse for every | >.
PHY 215A, Quantum Mechanics: Homework Set #5
Due: Oct.
27, 2016
1. Bound State for Two -function Potentials. 25 points.
(a) For a particle in 1D, calculate the ground state energy and wavefunction for equal strength,
attractive -function potentials, place
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PHY 215A, Quantum Mechanics: Homework Set #2
Due: Oct.
6, 2016
1. (6 points) Delta and Theta
Consider the function
(x y) = 0, x < y,
= 1, x > y.
(1)
Show that
d
(x y) (x y),
dx
(2)
i.e. this function satisfies the properties of the Dirac function.
2. (6 p
UC DAVIS PHYSICS PRELIM 2014 SOLUTIONS
1. Consider the following system of two masses and three springs, held between two immobile
walls. The left two springs are identical, and you should ignore gravity.
a) For each of the following cases, what are the n
Physics 215A; Quantum Mechanics HW 0 Solutions
1. 8 points. It is of course not necessary to obtain the exact form given below for the more involved manipulations.
~ i~k~r = ( , , )ei~k~r = (ikx , iky , ikz )ei~k~r = i~kei~k~r
e
x y z
~ 2 ei~k~r =
~ e
~
PHY 215A, Quantum Mechanics: Solutions to Homework Set #2
1. Delta and Theta.
R +|b|
The function satisfies (1)(x) = 0 for x 6= 0 and (2) |a| (x) = 1 for any a, b 6= 0. The function
satisfies these properties: You can integrate by parts to verify the seco
PHY 215A, Quantum Mechanics: Homework Set #3
Due: Oct.
13, 2016
1. 7 points. Canonical coordinates and canonical transformations.
(a) Show that the polar variables
p
= tan1 xy ,
= x2 + y 2 ,
xpx + ypy
p = e p~ = p
, p = xpy ypx ,
x2 + y 2
are canonical