The Handbook of Mathematics, Physics and
Astronomy Data is provided
KEELE UNIVERSITY
EXAMINATIONS, 2016/17
Level II (FHEQ Level 5)
Monday 9th JANUARY 2017, 09:15 – 11:15
PHYSICS/ASTROPHYSICS
PHY-20006
QUANTUM MECHANICS
Candidates should attempt ALL of PART A
and TWO questions from PART B.
PART A yields 40% of the marks, PART B yields 60%.
A sheet of useful formulae can be found on page 9.
NOT TO BE REMOVED FROM THE EXAMINATION HALL
PHY-20006 Page 1 of 9
, PART A Answer all TEN questions
A1 A particle is described by a wave function, Ψ(r, φ, z, t) in cylindrical
polar coordinates. Give an expression for the probability of observ-
ing the particle within a distance R from the z axis. [4]
A2 The solutions of the time-independent Schrödinger equation for a
particle in a ring have the form
1
ψ(θ) = √ eikθ .
2π
What are the allowed values of k? Justify your answer.
(Hint: consider the value of this function at θ + 2π.) [4]
A3 Calculate the value of A that normalizes the following solution of
the time-independent Schrödinger equation.
0 x ≤ −1
ψ(x) = A(1 − x2 ) −1 < x < 1
0 x≥1
[4]
/Cont’d
PHY-20006 Page 2 of 9
Astronomy Data is provided
KEELE UNIVERSITY
EXAMINATIONS, 2016/17
Level II (FHEQ Level 5)
Monday 9th JANUARY 2017, 09:15 – 11:15
PHYSICS/ASTROPHYSICS
PHY-20006
QUANTUM MECHANICS
Candidates should attempt ALL of PART A
and TWO questions from PART B.
PART A yields 40% of the marks, PART B yields 60%.
A sheet of useful formulae can be found on page 9.
NOT TO BE REMOVED FROM THE EXAMINATION HALL
PHY-20006 Page 1 of 9
, PART A Answer all TEN questions
A1 A particle is described by a wave function, Ψ(r, φ, z, t) in cylindrical
polar coordinates. Give an expression for the probability of observ-
ing the particle within a distance R from the z axis. [4]
A2 The solutions of the time-independent Schrödinger equation for a
particle in a ring have the form
1
ψ(θ) = √ eikθ .
2π
What are the allowed values of k? Justify your answer.
(Hint: consider the value of this function at θ + 2π.) [4]
A3 Calculate the value of A that normalizes the following solution of
the time-independent Schrödinger equation.
0 x ≤ −1
ψ(x) = A(1 − x2 ) −1 < x < 1
0 x≥1
[4]
/Cont’d
PHY-20006 Page 2 of 9
