PHYS 372 Quantum Mechanics A Assignment 3
Due February 7 2012, by 16:30
1. Consider a vector space consisting of onedimensional square integrable wavefunctions
\II(:1:, t). Note that as a consequence of being square integrable, these functions must
vani
University of Alberta
Department of Physics
Phys 372 Midterm Examination
Feb. 16, 2017, 9:30  10:50 am
Van Vliet 2215
Marsiglio
No aids and no calculator. Some formulas are attached. Do all 4 questions. They
are worth varying amounts as indicated (marks
Phys 372 Assignment 5 Due Tuesday Feb.14, 2017, before 9:30 am Marsiglio, Winter
2017
1. We want to study the solutions for a double square well. There are many examples
one can choose from, but perhaps the simplest is defined as follows: start with an in
Phys 372 Assignment 9
Due Mar. 23, 2017, before 9:30 am
Marsiglio, Winter 2017
, to f m , we get something
1. (a) Upon applying the raising or lowering operator, L
`
proportional to f`m1 , i.e.
f m = Am f m1 .
L
`
`, `
By demanding that both f`m and f`m
371 sum 4:. ,7 L 2017 .,
4. .  $004: gcAc&1k&c4&= . c + c g M *
LI) :0 [AI=0 :. QM
_ . :C
I. a Tim? AL, 1' 2,. '. A' y, LCAly El).
millmam A a. a;
7
M W)
='BCnB+CB

m= m ,_, 1.1 m 5.
.mtllMF >6; 4. A
u
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Phys 372 Assignment 8
Due Mar.16, 2017, before 9:30 am
Marsiglio, Winter 2017
1. Consider the problem discussed in class a harmonic oscillator potential, centred
at x = a/2, and imbedded in an infinite square well potential: V (x) = 12 m0 2 (x
a/2)2 (x)(
University of Alberta
Department of Physics
Phys 372 Midterm Examination
Feb. 11, 2016, 9:30  10:50 am
CCIS L1047
Marsiglio
No aids and no calculator. Some formulas are attached. Do all 5 questions. They are
worth varying amounts as indicated you should
Aid sheet for Phys372 Final, 2016. Not to be brought to the final  it will be provided.
We will use the notation that a+ a
is the raising operator and a a
is the lowering
operator.
For the one dimensional harmonic oscillator, with potential V (x) = 21
University of Alberta
Department of Physics
Phys 372 Midterm Examination Aid Sheet
Feb. 11, 2016, 9:30  10:50 am
CCIS L1047
Z
hQ(x, p)i
Marsiglio
dx (x)Q(x)
We will use the notation that a+ a
is the raising operator and a a
is the lowering
operator.
University of Alberta
Department of Physics
Phys 372 Midterm Examination Aid Sheet
Feb. 16, 2017, 9:30  10:50 am
Van Vliet 2215
Z
hQ(x, p)i
Marsiglio
dx (x)Q(x)
We will use the notation that a+ a
is the raising operator and a a
is the lowering
operat
Mg)
PHYS 372
Quantum Mechanics A
R. Marchand
CEB 442
Midterm Exam 2
March 11 2010
9:30 10:50
0 This exam is worth 20% of the nal mark.
a This is a closed book, closed notes exam.
Answer all questions.
0 Explain the steps of your derivations.
0 In
PHYS 372
Quantum Mechanics A
o This exam is worth 20% of the nai mark.
Midterm Exam 2
March 10 2011
1%
a This is a Closed book2 closed notes exam.
o Answer all questions.
0 Explain the steps of your derivations.
Rt Marchand
CEB 255
0 Include phys
PHYS 372 Midterm Exam 1 R. Marchand
Quantum Mechanics A February 2 2012 V103
10:00  10:50
0 This exam is worth 15% of the nal mark.
I This is a closed book, closed notes exam.
0 Answer all questions.
0 Explain the steps of your derivations.
0 Inclu
Phys 372 Assign. 1
Due Jan.19, 2017, in class, * before 9:30 am *
Marsiglio 2017
Note: sloppily done work is more likely to result in a lower grade than work that is done
neatly. The marker has limited time, and if he/she cannot see the process and answer
PHYS 372 Quantum Mechanics A Assignment 2
Due January 30 2012, by 16:30
1. Using the denition of the adjoint of an operator and the properties of the inner product
given in the notes, prove that for any operatorA, (Al):r = A
2. Consider a wave packet de
PHYS 372 Quantum Mechanics A Assignment 4
Due February 14 2011, by 16:30
1. Physical observable
Considering that
o a physical observable must be real,
0 observables are associated with operators for which the expectation value gives
the expectation val
SI
kCuA
kw 
RbM/(dy
7.
tn
66
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Mo.
FLQfJL 1m?
m 24
Had5i
Aha. t V020 E0 00.0136 1) J4)? Vd<g3 E0>Va 6 W
(c3 Vrm aw cfw_2.7%, > L w) 2 mg m 2.4M
Lavtan S a a: 21. $0) )_1 wwlwamu w
I L  2) 5 7.
W& E1 7 E: bf 2C 1) I
C? Q35?
(0) 13? Q Ma m 5":
Phys 372 Assignment 7
Due Mar. 9, 2017, before 9:30 am
Marsiglio, Winter 2017
1. (a) For operators A, B, and C show that [AB, C] = A[B, C] + [A, C]B.
(b) Assume that both operators A and B commute with their commutator, C = [A, B].
Show that
[A, F (B)] =
Phys 372 Assignment 4
Due Feb. 9, 2017, before 9:30 am
Marsiglio, Winter 2017
1. Use the recursion relation (hopefully) derived in class for the coefficients of the power
series for the harmonic oscillator problem,
aj+2 =
2(n j)
aj ,
(j + 1)(j + 2)
to ob
Phys 372 Assignment 10
Due Mar. 30, 2017 before 9:30 am
Marsiglio Winter 2017
This version (Mar. 28, 2017) has some modifications compared with the first; note
the change in sign convention in Prob. 2b.
1. Redo the finite spherical well problem, and deter
Phys 372 Assignment 2
Due Jan.26, 2017, before 9:30 am
Marsiglio, Winter 2017
If you use an integral from the internet or from a table in a book, you must quote the
source!
1. Show that the separation constant E discussed in Tuesdays lecture must be real.