Physics 410 practice problems for Final Exam Fall 2007, Frey Closed book exam. No calculators. 1. Consider the Sturm-Liouville equation Lui (x) + i w(x)ui (x) = 0. L is Hermitian over the interval [a, b] if
b a
u Luj dx = i
b a
uj (Lui ) dx
(a) Express th
Lectures 1-2
Systems of Linear Equations
matrix mult: cij =
k aik bkj
homog. and non-homog. cases determinant
matrix inversion
Orthogonal and unitary matrices
U U = U = U 1
|x
= U |x , x |x
= x|x
1
Lectures 3-4
Similarity transform.: A = SAS 1
Th
Physics 410 Midterm Practice Exam
Fall 2007, Frey
Closed book exam. No calculators. There are 6 practice problems. The actual exam will have
no more than 5.
1. (15 points)
Using the denition of matrix multiplication, show that (AB) = B A .
2. (25 points)
Physics 410 practice problems for Final Exam
Fall 2007, Frey
Closed book exam. No calculators.
1. Consider the Sturm-Liouville equation Lui (x) + i w(x)ui (x) = 0. L is Hermitian over the
interval [a, b] if
b
a
u Luj dx =
i
b
a
uj (Lui ) dx
(a) Express th
Lectures 1-2
Systems of Linear Equations
matrix mult: cij =
k aik bkj
homog. and non-homog. cases determinant
matrix inversion
Orthogonal and unitary matrices
U U = U = U 1
|x
= U |x , x |x
= x|x
1