The chapter numbers are from Griffiths unless otherwise indicated.
Due ch:
6 Sep 1-1, 3, 6, 7
#1 Complete derivation of stated identity.
For three sets of boundary conditions, find all the
solutions and use each to get the corresponding
Fourier series for f( x ) = x ( 0 < x < L )
u( 0 ) = 0 = u( L )
u'( 0 ) = 0 = u'( L )
u( 0 ) = 0 = u'( L )
Also sketch and analyze the results.
16 Sep 1-4, 8, 9, 13
#2 2-3, 5
Schaum: 7-31, 32 AND IN BOTH CASES put in context
of boundary conditions on u'' = lu
23 Sep 1-14
#3 2-2, 6, 7, 15, 16
Schaum: 7-42
Math Preliminaries: 9, 10, 11
2 Oct 2-8, 13, 17, 19, 21
#4 Math Preliminaries: 18, 19, 20
Parity operator on eigenfuntions of energy
for the infinite square well.
(Pg)( x ) = g( L - x )
[IS this the parity operator?]
9 Oct 2-10, 12, 23, 24, 31, 37
#5 3-1, 2
Math Preliminaries: 21
Repeat the derivation of the identity that is the
core of Fourier series, but do it for
the Schroedinger equation instead of for
u'' = lu.
21 Oct 2-28, 30, 36, 41
#6 3-9, 11, 17
Vector Space Notes: 3, 5, 8
5 Nov START FROM THE DEFINITION of the components of
#7 an operator and of linearity:
Compute the components of the composition of two
such operators and express the results in
terms of those in the two given functions.
Apply this to the rotation example.
The vector space of cubic polynomials. d/dx is
an operator (check). Pick a basis and compute
its components.
Do the same for d2/dx2 and then
compare the results of the previous problem.
The vector space of square-integrable and differentiable
functions on 0<x<L and use as a basis the
eigenfunctions of H for the infinite square well.
Compute the components of H.
Classical angular momentum for a point mass is rxp [I'm
dropping the vectors here. They're hard to put in.]
For many masses it is a sum of such terms. A rigid body is
rotating about a fixed axis with angular velocity
omega. The total angular momentum is a sum (or
integral) over rx(wxr) dm.
Compute the components of this function of omega
in a common orthonormal basis.
3-25, 39, 41, 42
2-43
20 Nov Repeat the components of d/dx on cubic polynomials, but use
#8 as a basis the Legendre polynomials. Same for second
derivative and check for product.
Prove that the inertia operator is Hermitian.
Complete the derivation of the Lz in terms of
theta and phi.
4-14, 24
9 Nov 4-17, 26, 27, 28, 33, 39
#9