


PCS400 W2017 Exam Phys  FS.pdf
PCS400_W2017_Exam_Phys__FS.pdf
Showing 12 out of 4
PCS400 W2017 Exam Phys  FS.pdfFinal Examination ...
PCS400_W2017_Exam_Phys__FS.pdfFinal Examination Page of 1 28
PCS400 W2017 Exam Phys  FS.pdfFin...
PCS400_W2017_Exam_Phys__FS.pdfFinal Examination Page of 1 28
Page 1
Final Examination
Page of
1
28
Student No.: ____________________
Student Name: ____________________________________
PCS 400
Quantum Mechanics I
(Physics Stream)
•
This is a closedbook Examination. You have
3 hours
to answer all the questions.
•
This Examination consists of 7 questions. The weight of each question and each
subquestion is listed on the left margin.
•
You need to answer 6 of the 7 questions.
You can answer all the questions if you
would like.
If you do answer all the questions,
the best 6
answers
will be chosen for the mark of the Examination.
•
A
3page formula sheet
is attached at the end of the Quiz
booklet as well as a sheet with integrals and expressions
relevant to three of the problems. Please detach these
pages for use during the Examination. No other page(s) in
the Quiz booklet can be detached. No other aids are
permitted.
You are allowed to use ONLY the formula
sheet provided with the Quiz.
In particular, the
preliminary formula sheet posted in D2L is not allowed.
•
IMPORTANT:
You MUST provide a derivation of the
answer to each question. If no work or correct argument is
shown, the mark for the question may be zero, even if the
answer is correct.
•
You have at your disposal empty Utility pages following
each of the questions as well as empty Additional Utility
pages at the end of the exam booklet. You can use these for
derivations or for rough work. If the derivation of the
answer to a question is continued on one of the Additional
Utility pages,
please write a note to that effect
as they
might not be considered for marking otherwise.
•
Make sure that you have all pages with all 7 questions
before you start. Inform the invigilator if your booklet is
missing pages.
Ryerson University
Department of Physics
PCS 400 – Quantum Mechanics I
Final Examination
April 17, 2017
3:00 pm to 6:00 pm
TRS 1075
1
/40
2
/40
3
/40
4
/40
5
/40
6
/40
7
/40
/240
%
Page 2
Formulas and Constants
Part 1
PCS 400
Quantum Mechanics 1
h
=
6.63
×
10
−
34
J
⋅
s
=
4.14
×
10
−
15
eV
⋅
s
!
=
h
2
π
=
1.055
×
10
−
34
J
⋅
s
=
6.58
×
10
−
16
eV
⋅
s
1 eV
=
1.602
×
10
−
19
J
1 J
=
6.242
×
10
18
eV
z
=
a
+
ib
⇒
z
*
=
a
−
ib
e
i
θ
=
cos
θ
+
i
sin
θ
1
i
=
−
i
i
!
∂
∂
t
Ψ
(
x
,
t
)
=
−
!
2
2
m
∂
2
∂
x
2
Ψ
(
x
,
t
)
+
V
(
x
)
Ψ
(
x
,
t
)
Ψ
(
x
,
t
)
=
ψ
(
x
).
e
−
i
E
!
t
−
!
2
2
m
d
2
dx
2
ψ
(
x
)
+
V
(
x
)
ψ
(
x
)
=
E
ψ
(
x
)
ˆ
p
x
2
=
−
!
2
∂
2
∂
x
2
ˆ
p
x
=
−
i
!
∂
∂
x
ˆ
H
Ψ
=
E
Ψ
ˆ
H
=
−
!
2
2
m
∂
2
∂
x
2
+
V
(
x
)
ˆ
H
=
i
!
∂
∂
t
ˆ
p
x
=
Ψ
*ˆ
p
x
Ψ
dx
−∞
∞
∫
ˆ
H
=
Ψ
*
ˆ
H
Ψ
dx
−∞
∞
∫
Δ
p
x
Δ
x
≥
!
2
P
(
x
,
t
)
=
Ψ
*(
x
,
t
)
Ψ
(
x
,
t
)
=
Ψ
2
Ψ
*
Ψ
dx
−∞
∞
∫
=
Ψ
2
dx
−∞
∞
⌠
⌡
=
1
P
(
a
≤
x
≤
b
)
=
Ψ
*
Ψ
dx
a
b
∫
Δ
x
=
x
2
−
x
2
x
2
=
Ψ
*
x
2
Ψ
dx
−∞
∞
∫
x
=
Ψ
*
x
Ψ
dx
−∞
∞
∫
Δ
p
x
=
ˆ
p
x
2
−
ˆ
p
x
2
ˆ
p
x
2
=
Ψ
*ˆ
p
x
2
Ψ
dx
−∞
∞
∫
V
(
x
)
=
0
for
0
≤
x
≤
a
∞
otherwise
⎧
⎨
⎪
⎩
⎪
ψ
n
(
x
)
=
2
a
sin
n
π
a
x
⎛
⎝
⎜
⎞
⎠
⎟
E
n
=
!
2
π
2
2
ma
2
n
2
=
h
2
8
ma
2
n
2
Ace your assessments! Get Better Grades
Browse thousands of Study Materials & Solutions from your Favorite Schools
Ryerson University
Ryerson_University
School:
Quantum_Physics_I
Course:
Introducing Study Plan
Using AI Tools to Help you understand and remember your course concepts better and faster than any other resource.
Find the best videos to learn every concept in that course from Youtube and Tiktok without searching.
Save All Relavent Videos & Materials and access anytime and anywhere
Prepare Smart and Guarantee better grades
Students also viewed documents
lab 18.docx
lab_18.docx
Course
Course
3
Module5QuizSTA2023.d...
Module5QuizSTA2023.docx.docx
Course
Course
10
Week 7 Test Math302....
Week_7_Test_Math302.docx.docx
Course
Course
30
Chapter 1 Assigment ...
Chapter_1_Assigment_Questions.docx.docx
Course
Course
5
Week 4 tests.docx.do...
Week_4_tests.docx.docx
Course
Course
23
Week 6 tests.docx.do...
Week_6_tests.docx.docx
Course
Course
106