0.1
Maxwell equations
It is an experimental fact that the force acting on a point charge due to the
electromagnetic field is given (in Gaussian units) by:
~v
~
~
~
F = m~a = q E + B
(1)
c
~ B.
~
In order to solve this equation it is necessary to know the
Dr. S Kuhn
Grad Quantum I Lecture 4
6Sept12
Infinite Vector Space (Shankar, p. 57)
Infinite vector space implies infinite dimensions
Example: f : [0, 2] C
requirement:f (0) = f (2) , f continuous
In between, a function can do anything, but we assume its
Dr. S Kuhn
Grad Quantum I Lecture 3
4Sept12
Operators
Operator can be represented by its matrix elements.
ij =< i|j >
: V V
Hermitian
= ; ij = ji
Unitary
U: VV
U U = U U = 1
hU w|UP
vi = hw|U U |vi = hw|1|vi = hw|vi operator acting on vectors w and v
j
PHYSICS 621 - Fall Semester 2013 - ODU
Graduate Quantum Mechanics - Problem Set 3
Problem 1)
" 0 0 1 %
$
'
Consider the matrix = $ 0 0 0 ' .
$ 1 0 0 '
#
&
i)
ii)
iii)
iv)
Is it hermitian?
Find its eigenvalues and eigenvectors
Verify that UU is diagonal, U
PHYSICS 621 - Fall Semester 2013 - ODU
Graduate Quantum Mechanics - Problem Set 6
Problem 1)
The normalized wave function (x, t) satisfies the time-dependent Schrdinger equation for a free
particle of mass m, moving along the x-axis (in 1 dimension). Cons
PHYSICS 621 - Fall Semester 2013 - ODU
Graduate Quantum Mechanics - Problem Set 5
Problem 1)
An operator A, corresponding to a physical observable, has two normalized eigenstates 1 and 2
with non-degenerate eigenvalues a1 and a2, respectively. A second op
PHYSICS 621 - Fall Semester 2012 - ODU
Graduate Quantum Mechanics - Problem Set 1
Problem 1)
Write down the total mechanical energy (kinetic plus potential) of a mass m in free fall, expressing it in
terms of the momentum p and the height x above ground:
Classical Mechanics (in about an hour)
There are two key concepts to cover in classical mechanics that will apply to our understanding of quantum mechanics. They are the Lagrangian L and the Hamiltonion H.
We start off easy by looking at Newtons Law in 1
PHYSICS 621 - Fall Semester 2013 - ODU
Graduate Quantum Mechanics - Problem Set 4
Problem 1)
Assuming a particle is described with the usual cartesian coordinates (x,y,z) and momenta (px, py, pz).
Write down the x, y and z components of the angular moment
PHYSICS 621 - Fall Semester 2013 - ODU
Graduate Quantum Mechanics - Problem Set 2
Problem 1)
Do continuous functions defined on the interval [0L] and that vanish at the end points x = 0 and x = L
form a vector space? How about periodic functions obeying f