PHY- Exam Paper

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