Homework Assignment 1 Updated
Physics 501
Due September 20, 2010 by noon
1. Prove the following two Dirac delta function identities.
(ax) = (x)/|a|
(f (x) =
i
(x ai )
|df /dx|x=ai
f (x) (x) dx = f
Lecture 26
The Hydrogen Atom
December 8, 2010
Lecture 26
Review of Spherically Symmetric Potentials
"
#
2
h
2m
2
+ V (r ) E Elm(r, , ) = 0
Elm(r, , ) = REl (r )Ylm(, )
"
2
h 1d
2m r 2 dr
r
2
d
dr
+
RE
Lecture 22
Rotations in Thrree Dimensions
November 22, 2010
Lecture 22
Rotations in Three Dimensions
Now we need to consider rotations
about three axes: x, y and z .
Just as Lz generates rotations abo
Lecture 21
Rotations in Two Dimensions
November 17, 2010
Lecture 21
Spatial Translations in Two Dimensions
px generates translations in the x direction
py generates translations in the y direction
Tra
Lecture 20
Parity and Time Reversal
November 15, 2009
Lecture 20
Time Translation
| (t + ) = U [T ( )] | (t) =
H
i
I H | (t)
h
is the generator of time translations.
i
U [T ( )] = I H
h
[H, H ] = 0
al
Lecture 19
Transformations
November 10, 2010
Lecture 19
Transformations
We are now going to study transformations and
their relationship with symmetries, invariance of the
equation of motion under the
Lecture 18
The Harmonic Oscillator Revisited
November 8, 2010
Lecture 18
Harmonic Oscillator Again
Review of wave function solution
i (x, t) =
h
t
1
h
2 2
+ m 2x2 (x, t)
2m x2
2
energy eigenstates
2
Homework Assignment 6
Physics 501
Due Nov 11, 2010 by 3 pm
1. a) Solve the radial time-independent Schrodinger equation for the two-dimensional isotropic
harmonic oscillator.
h
2
2m
1d
d2
+
2
d
d
+
1
Homework Assignment 5
Physics 501
Due October 28, 2010 by 3 pm
1. Consider a particle of mass m in an innite one-dimensional potential well V (x) given by
V =0
for
|x| a
V =
for
|x| > a
a) Find x for
Homework Assignment 4
Physics 501
Due October 18, 2010
1. Consider the vector space of complex-valued functions of one real variable, | with x| =
(x). Show that the normalization | is the same in bot
Homework Assignment 3
Physics 501
Due October 11, 2010
1. Starting with the set of basis vectors
3
|I = 0
0
0
|II = 1
2
0
|III = 2
5
nd an orthonormal basis using the Gram-Schmidt procedure.
1
2
2. a)
Revised Homework Assignment 2
Physics 501
Due September 30, 2010
1. For the state specied by:
show that
2
x2 = x + a2
x =a
p = i
h
and using the momentum operator
show that
1/4 (xa)2 /4 2
1
x
e
2 2
(
Lecture 27
More on the Hydrogen Atom
December 13, 2010
Lecture 27
Size of the Hydrogen Atom
general form of energy eigenstate wave function
unlm(r, , ) = Rnl (r )Ylm(, )
unlm(r, , )
r
na0
l "nX1
l
ak