PHYS126 Spring 2011 Homework 2 Due Feb 18, beginning of lecture. 1. An airline, all the planes fly with an airspeed of 500km/h, serves three cities, A, B and C, where B is 500km due east of A, and C is 500km due north of A. On a certain day, there is a st
Solution to Homework 1 Let c = speed of the swimmer in still water v = velocity of water current L = distance between starting and end points t1 = roundtrip time swimming along the river current t2 = roundtrip time across the river current
Round trip of t
Let c = speed of the swimmer in still water v = velocity of water current L = distance between starting and end points t1 = roundtrip time swimming along the river current t2 = roundtrip time across the river current Show in general, using classical veloc
PHYS126 Supplementary Notes 7
You will have a mid-term exam this week and Prof. Du has made the mid-term review in the lecture. So I just show some problems to you to review how to solve the problems. Please notice that the note will not cover the short a
PHYS126 Supplementary Notes 6
1. De Broglies Hypothesis
E = hf or
E=
and p = and p = f k
h = h 2
where h = 6.63 10 34 J .s = 4.14 10 15 eV .s Example: Find the wavelength of an electron with energy E = 2MeV Hint: The De Broglie relation = h / p is correc
PHYS126 Supplementary Notes 5
1 Feel the number connecting the macroscopic world and microscopic world. How many C atoms are there in (a) 1 g of CO2 (b) 1 mole of CH4 (c) 1 k mole of C2H6 a) 1g of CO2 Number of moles of 1g CO2 = 1/(12+2 x 16) = 1/44 There
PHYS126SupplementaryNotes4 ImportantFormulaformassenergyrelation PythagoreanTheorem:
Combining
and
,wecanget
CaseStudy:MasslessParticles Isthereanymasslessparticlewhichisstationary?No From Whichimplies Thatsphoton. Example Aneutralpiontravelingalongthexax
PHYS126 Supplementary Notes 3
In recent lectures, we have learnt several concepts of special relativity. In this note, several exercises of each topic are shown. 1. Lorentz transformation Now, define two inertial frames S and S. Frame S moves in the +x di
PHYS126 Spring 2011 Homework 2 Solution t ABA = 2L 2(500) = = 2.0833hr 2 v 1002 c 1 2 500 1 2 c 500 2L 2(500) = = = 2.0412hr 2 v 1002 c 1 2 500 1 c 5002
1. (a)
(b)
t ACA
2. Consider the figure in Lecture 2 note slide #37, suppose there are two frames S an
PHYS126 Spring 2011 Homework 3 Due Feb 25, beginning of lecture.
1. Beiser (textbook), Chapter 1, Exercise 21.
2. Lecture 3: Slide #28 We have shown that when measured at t = 0 in cfw_s, length contraction results. We now decide to do this length measurem
P HYS126 HW6 Solution 1. Solution A. By using
B.
Inverse the equation to get W hen n =2, W hen n =3, For n>3, , t he solution does not exist.
2. Solution A. As the object is a blackbody, assume all the energy and momentum of photon are absorbed perfectly
PHYS126 Spring 2011 Homework 6, Due March 18, beginning of lecture.
1. X-rays of wavelength 0.2 nm are diffracted off a crystal. The first order Bragg maximum is measured at a glancing angle of 17.5 degrees. (a) What is the spacing of the planes that are
1
a for long wavelengths, hc / k BT = 1
hc / k BT
So e
1 = hc / k BT
2 hc 2 1 2 hc 2 k BT 2 ck BT I = = = 5 e hc / kBT 1 5 hc 4
20
15
10
5
0
1
2
3
4
5
6
The red one is Rayleigh-Jeans function, the Blue one is Planck distribution. The X axis is the wavele
PHYS126 Spring 2011 Homework 5, Due March 11, beginning of lecture. In the following,
h = Plancks constant; c = Speed of light; kB = Boltzmann constant.
In lecture, we described the Planck distribution function for blackbody radiation using the frequency
Homework 4 solution 1a) = 2 m 2 v 2 c 2 + m 2 c 4 = ( 2 v 2 + c 2 )(mc) 2
v2 c2 =( + c 2 )(mc )2 = ( 2 2 )(mc) 2 v2 c v 1 2 c 2 =E
b) E = 2+4 = 6GeV p = 4*2^0.5 GeV/c v/c = pc/E v = 2*2^0.5 *c/3 = 0.943c E = E pi + E p
2a)
1116 2 + ( pc) 2 = 938 + 140 2 +
PHYS126 Spring 2011 Homework 4, Due March 4, beginning of lecture. 1a. In lecture, we proved ( pc) 2 + (mc 2 ) 2 = E 2 from the space-time relation. Prove this
v2 v2 1 2 c2 c into the right hand side. After some algebra, you will get the left hand side. 1
1.Solution: Take the spacecraft as the rest frame and the earth as the moving frame Assume the length of the antenna is L in the rest frame (spacecraft frame), Because the velocity of the spacecraft has no length contraction effect on the direction which
PHYS126 Supplementary Notes 2
In lecture 2 and 3, we have learnt some basic concepts of Special Relativity such as time dilation and Lorentz transformation. In this note, a simple derivation of time dilation and an example of loss of simultaneity are show
PHYS126 Supplementary Notes 1
In lecture 1, we have learnt the swimmer competition problem and the MichelsonMorley experiment. In this supplementary note, we try to relate these two situations and explain why Classical Mechanics has to be replaced by Spec
Physics 126 Lecture 5 Feb 21, 23, 2011
Suggested Reading: Chapter 1.5, 1.7 1.9
Twin paradox Conservation Laws in Special Relativity Einsteins definition of momentum E=mc2 : what does it mean? Space-time and energy-momentum Useful formulae and example
1 M.
Physics 126 Lecture 2
11 Feb. 2011 Relativity of Time Relativity of Simultaneity
Reading: Ch. 1.2 of Beiser
Outline: Michelson-Morley experiment Failure of classical velocity addition formula Special Relativity: Einsteins Two Postulates Time dilation Loss
Physics 126 Spring 2011 Introduction to Modern Physics Grading Scheme
Home work Quiz in tutorial PRS in lecture Midterm Final 10% 8% 2% 35% 45%
http:/teaching.phys.ust.hk/phys126/course_info.htm
H. B. Chan
1
Physics 126 Spring 2011 Homework
Home work 10%
Lecture 16: The Schrodinger Equation in 1D
01 April, 2011 1. The Schrodinger equation in 1D: p2 ih ( x , t ) = x + U ( x ) ( x , t ) t 2m
(16-1)
Recall: p x =
h , we have: i x h2 2 ih ( x , t ) = + U ( x ) ( x, t ) 2 t 2m x
Classical Mechanics: d2 F =
Lecture 15: Introduction to Quantum Mechanics
Shengwang Du, 28&30 March 2011 [Powerpoint slides: introduction] 1. Classical (Relativity) versus quantum way of thinking Newtonian Mechanics: r r d 2r r Motion equation: F = ma = m 2 dt r r r r Initial condit
Lecture 14: Complex Variable and Analysis
(Mathematic Preparation for Quantum Mechanics) Shengwang Du, 25 March 2011 1. Representation of complex numbers ( z C ) Complex number: z = a + ib with a & b R (both a and b are real numbers) where the imaginary n
Midterm Exam Exam will be Saturday, 26 March, 2011, LTJ, 2:30 to 5:00 pm Arrive early. Seats will be assigned. Check before you enter. The exam will cover up to and including Lecture 12. Physical constants will be provided. Bring your own calculator
1
Phy
PHYS126 Fall 2011 HW #8 Due 01 April
1) Show that the following function of general sinusoidal wave ( x) = a sin(kx) + b cos(kx) is equivalent to the following expression ( x) = Ae ikx + Be ikx . Please also give expressions for A and B in terms of a and
Physics 126 Lecture 6 Feb 25, 2011
Suggested Reading: Chapter 1.8 1.10
E=mc2 : what does it mean? Space-time and energy-momentum Useful formulae and example
1 M.Loy, H. B. Chan
Collision of two particles with identical mass m
Frame S
uy = uy vxu x
Frame