QMUL, School of Physics and Astronomy
Date: 23/01/2017
SPA4122 Mathematical Techniques 2
Exercise Class Script 2: Coordinate Systems and Double Integrals
1. [*] Calculate the integral:
ZZ
xy dxdy
I=
A
where the area A is defined as:
A = (x, y) R2 : x >
QMUL, School of Physics
SPA4122 Mathematical Techniques 2
Problem Sheet 2: Coordinate Systems and Integrals
Date issued: 19/01/2017
Hand in: 16:00, Thursday 26/01/2017
1. [*] Consider the integral:
ZZ
xy dxdy
I=
A
where the area A is defined as:
A = (x,
Quantum Physics PHY4215 - Homework 1
1. Explain what is a black body ? What is the spectral emittance of an object ? [5+5]
2. The Planck blackbody radiation spectrum is given by
R(, T ) =
2hc2
1
hc
5
e kT 1
Derive Stefans Law for the total Power radiated
MT2 Lectures: week 1
January 12, 2017
1
Basics
1.1
Revision
Things that we will not mention but students are assumed to know:
1. square of a binomial:
(a + b)2 = a2 + 2ab + b2
2. difference of squares:
(a + b)(a b) = a2 b2
3. real and imaginary parts of c
SPECIAL RELATIVITY
Albert EINSTEIN introduced his SPECIAL THEORY OF RELATIVITY in 1905. To
understand the theory, we will first review the background, the theoretical and
experimental developments since Newton.
SPECIAL means just, not general. The theory
Quantum Physics Some part A type revision questions, mostly on the
Schr
odinger equation (with solutions)
A1. Let (x) = A(x a)(x b) the wavefunction of a particle which is confined to
move freely in the one-dimensional interval 2 x 2 (in other words, the
@ Queen Mary
University of London
BSc and MSci EXAMINATION
PHY215 Quantum Physics
Time Allowed: 2 hours 15 minutes
Date: 5 May 2004
Time: 10:00
Instructions: Answer THREE QUESTIONS only. Each ques-
tion carries 25 marks. An indicative marking
scheme is sh
Q Queen Mary
University of London
BSc and MSci EXAMINATION
PI-IY-215 Quantum Physics
Time Allowed: 2 hours 15 minutes
Date: 13 May 2005
Time: 10.00
Instructions: ANSWER ALL QUESTIONS IN SECTION A.
Each question carries 10 marks. An indicative
marking-sche
BSc/MSci MidTerm Test
PHY4217
Waves and Oscillations
Time Allowed:
50 minutes
Date:
13th Nov, 2012
Time: 9:05 - 9:55
Instructions:
Answer ALL questions in section A. Answer ONLY ONE questions from section B. Section A carries 25 marks, each question
in se
QMUL, School of Physics
SPA4122 Mathematical Techniques 2
Problem Sheet 1: Complex Numbers
Date issued: 12/01/2017
Hand in: 16:00, Thursday 19/01/2017
1. [*] Write in the algebraic form c = a + ib, the following complex number:
(2 + i)(1 i)
(3 2i)
[4 Mark
Quantum Physics SPA4215 - Homework 2
1. Summarize, in your own words, the key ideas in the derivation of the Rayleign Jeans
Law. Your answer should be less than a page long and include qualitative description as well
as a few equations.
[10]
2*. The avera
Electromagne,c radia,on
Observa,onal astronomy concerns the detec,on
and analysis of electromagne,c radia,on across the
spectrum, from the shortest wavelength gamma rays
through to long wavelength radio waves.
Electromagn
Our Universe
SPA-4101"
Synopsis
This module provides an introduc5on to modern
astronomy and astrophysics
Topics covered include an introduc5on to the history of
the subject (da5ng back to ancient greek astronomers),
the
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QMUL, School of Physics and Astronomy
Date: 16/01/2017
SPA4122 Mathematical Techniques 2
Exercise Class Script 1: Complex Numbers
1. [*] Verify that z = 1 + i is a solution of the polynomial P (z) = z 4 5z 3 + 10z 2
10z + 4. Calculate then all the roots
Quantum Physics PHY4215 - Exercise Sheet 5
1. The Gaussian wavepacket is a wave with variable amplitude
(x) k0 ,d (x) =
2
1
ik0 x x 2
2d
e
1
4 d
Show that this is a normalized wavefunction, i.e.
Z
(x) (x)dx = 1
You may use the integral
Z
ax2
dx e
r
=
a
2
Electric and Magnetic Fields - Exercises 1
Chris White ([email protected])
Questions marked with () are meant to be more challenging. Please let me know of any typing errors and
/ or other mistakes.
1. Under what conditions is the dot product b
z
y
x
I
I
(a)
y
(b)
Figure 1: (a) An infinite sheet of current in the (x, y) plane; (b) a view looking down the x-axis, such that
the current is pointing towards us.
Electric and Magnetic Fields - Exercises 7
Chris White ([email protected])
Que
Our Universe
Coursework 7
Due in on Wednesday of week 9 at 16:00
Useful information
Boltzmanns constant k = 1.38 1023 J K1
Plancks constant h = 6.63 1034 m2 kg s1
Mass of hydrogen molecule mH2 = 3.34 1027 kg
Gravitational constant G = 6.67 1011 N kg2 m2
S
Our Universe
Coursework 4
Due in on Wednesday of week 5 at 16:00
Useful Information
Gravitational constant G = 6.67 1011 N m2 / kg2
Solar mass 1.98 1030 kg
Exercise class question - not to be handed in
Consider two solar-mass stars that are on circular
Our Universe
Coursework 6
Due in on Wednesday of week 8 at 16:00
Exercise class question - not to be handed in
The purpose of this question is to illustrate the fact that the tidal acceleration exerted by a central
star acting to tidally deform an orbitin
Our Universe
Coursework 8
Due in on Wednesday of week 10 at 16:00
Useful information
Boltzmanns constant k = 1.38 1023 J K1
Mass of hydrogen atom mH = 1.67 1027 kg
Gravitational constant G = 6.67 1011 N kg2 m2
Solar mass Msun = 2 1030 kg
Solar luminosity
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Our Universe
Coursework 5
Due in on Wednesday of week 6 at 16:00
Exercise class question - not to be handed in
The Earth spins on its axis once every 24 hours, and the Moon orbits the Earth once every 27.3
days. The mass of the Moon is 6.8 1022 kg, and th
Our Universe
Coursework 9
Not to be handed in - practice questions from weeks 11 and 12 of the lecture course
Useful information
Boltzmanns constant k = 1.38 1023 J K1
Mass of hydrogen atom mH = 1.67 1027 kg
Gravitational constant G = 6.67 1011 N kg2 m2
S
Electric and Magnetic Fields - Solutions 1
Chris White ([email protected])
1. The dot product between two vectors is zero if either of the vectors has zero magnitude, or if cos = 0,
where is the angle between them. This occurs if the vectors ar