PHYS126 Quiz 5 Solution
1. (a)
h2 d 2
+ U = E
2
2m dx
For 0 < x < L, U = 0
h2 d 2
= E
2m dx 2
d 2
= k 2 ,
dx 2
2
where k =
2mE
(1 pt)
h2
General solution is
( x) = A cos kx + B sin kx , where A and B are constants. (2 pts)
Boundary conditions: (0) = (
Solution to Quiz 1
(a) Along the water current, t1 =
L
L
2cL
+
=2
c + v c v c v2
(b) Across the water current, t 2 =
2L
c v2
2
2cL
2
t1
c
1
= c v =
=
= , so t1= t2
(c) t
2
2
2L
c v
v2
2
1 2
c2 v 2
c
2
PHYS126 Supplementary Notes 13
In this last tutorial note, we will focus on some typical examples of fermions and
bosons, Paulis exclusion principle, electron configuration and energies of elements in
periodic table, selection rule.
A.
Paulis exclusion pr
PHYS126 Tutorial Note
Hydrogen Atom Wavefunction
Outline of derivation of H-atom wavefunction
1. Start with Time independent Schrodinger Equation
2 2
+ =
2
2. Introduce Separable Solution: (r, , ) = R(r)()()
3. We can obtain three differential equations
PHYS126 Supplementary Notes 9
In lecture 18 and 19, we have learnt some examples of Schrdinger equation: 1D
infinite potential well, 1D finite potential well, 2D rigid box, 1D simple harmonic
oscillator; and also some new concepts such as quantum tunnelin
PHYS126 Supplementary Notes 12
Principal Quantum Number:
n = 1, 2,3, K
Orbital Quantum Number:
l = 0,1, 2,K ( n 1)
Magnetic Quantum Number:
ml = 0, 1, 2,K l
(s, p, d, f)
The interpretation of l and ml:
L = l ( l + 1) h
Angular Momentum:
Lz = ml h
z-compon
PHYS126 Supplementary Notes 8
A particle with mass m is confined inside in a rigid 1D box within a < x < a . At t = 0
, the particle initial wave function is 0 ( x) =
1
1
x
3 x
cos
cos
.
2a
2a
2a
2a
(a) Find the eigenstate and eigenvalue in this c
PHYS126 Supplementary Notes 10
3D Rigid Box
In lecture 19, we have solved the time independent Schrdinger equation for the eigen
wave function and energy for the 2D rigid box by using separation of variables.
Now lets do the 3D case.
U = outside
U = 0 ins
Eigen State of an Operator
r
r
Eigen equation: A a (r ) = a a (r )
r
a (r ) : Eigen state/function of the operator A with an eigen value of a
a : Eigen value
Physical meaning/property of the eigen state:
Expectation value:
r
r
r
*r
*r
*r
A = a (r ) A a
PHYS126 HW11 Solution
1. Given that
By separation of variable, put
, we can obtain:
Decouple the equation into
It is Time-independent Schrdinger equation (TISE) of 1D harmonic oscillator in direction x.
Similarly, TISE of y-direction and z-direction can b
PHYS126 Quiz 6 29-4-10
Time: 15mins
Name:
Student ID:
T
1. For 2p state (i.e. n = 2, l = 1), what is the magnitude of the angular momentum L?
What are the possible values of Lz ?
L = 1(1 + 1) = 2
L z = ,0,
2. Consider the hydrogen atom without spin, if a
i) Time dilation
Let event A and B in S frame are:
A: (0,0) B:(0, t)
Apply Lorentz Transform then we get event A and B in S frame:
Therefore, time dilation comes out
A:(0, 0) B: (-vt,t)
ii) Length contraction
In S frame:
A: (0,0) B: (L, 0)
In S frame:
A:
Muscles: For a long time, human muscles were the only prime mover.
Animal muscles were next added, supplemented by wheels and sails.
modern ones
Steam engines: improved by James Watt in the 1780s, convert the heat from
burning coal into mechanical energ
reduce the reliance
on fossil fuel
>prime mover
Electricity
Jet engine
Electricity
World Primary Energy Supply
Diesel
engine
Containership
Oil tanker
Electric
generator
Global energy consumption (1850-2000) and corresponding
technological inventions (Naki
Physics 1003
Lecture 2
Mr. Gary Kalong Ng
[email protected]
Room 4469, ext 7528
Outline
Growth of energy consumption; Population growth;
Exponential growth and multiplication (Doubling);
Generation and use of energy
1
Energy consumption for comfort of life
Amo
Nuclear Physics:
Radioactive Decay and
Radiation Absorption
Physics 127
Introduction to Modern
Physics Laboratory
Name: Li Pak Ho (1B)
Student ID: 08301735
Submission Date: 27th Apr, 2009
Introduction
Nuclear Physics is the study of the nucleus of an atom
Electrical Conduction in
Solids
Physics 127
Introduction to Modern
Physics Laboratory
Name: Li Pak Ho (1B)
Student ID: 08301735
Submission Date: 6th Apr, 2009
Introduction
We all know that different material have different conductivity but temperature can
Balmer Series:
Quantization of Atomic
Energy Levels
Physics 127
Introduction to Modern
Physics Laboratory
Name: Li Pak Ho
Student ID: 08301735
Submission Date: 23rd, Feb, 2009
Introduction
Several experimental observations stroke the development of quantu
Photoelectric Effect
Physics 127
Introduction to Modern
Physics Laboratory
Name: Li Pak Ho
Student ID: 08301735
Submission Date: 23rd, Feb, 2009
Introduction
W
hen radiation of sufficiently short wavelength interacts with metal,
electrons are knocked out
PHYS126 Quiz 3 11-3-2010
Time: 20min
Name:
Student ID:
1.
The rest energy of a certain nuclear particle is 8 GeV and its kinetic energy is 9GeV. Find its
momentum (in GeV/c) and speed (in c). (30 marks)
2.
X rays of wavelength 10.0 pm are scattered from a
1.Solution:
2.Solution:
a) For positive x, the quantum well potential is linear to the x. It is similar to the gravitational field
on the earth surface.
For negative x, the potential is infinite. Its impossible to find the particle in this region.
b)
3. S
Homework set 12 solution
1
The energy level for 1-D infinite potential well is given by
n 2 2 h2
E=
= n 2 E0 where E0 = 0.377eV
2
2ma
To excite a ground state electron in this system, the lowest level is 6, for the other lower
level is already filled with
PHYS126 Spring 2011 Homework 13 Solution
J ( J + 1)h2
Rotational energy eigenvalue is given by E =
2I
2
h
h
For J = 0 J = 1 absorption, E =
= h = 2 h I =
I
2
m12 C m16 O
12u 16u 48
12 16
=u
Reduced mass of C O = M =
m12 C + m16 O 12u + 16u 7
1.
h
2
The mo
Lecture 19: The 2D Schrdinger Equation
(Shengwang Du, 11&13 April 2011)
1. 2D Schrdinger Equation
Time-dependant Schrdinger equation
ih ( x, y, t ) = H ( x, y, t )
t
1
2 2
ih ( x , y , t ) =
[ p x + p y ] ( x, y, t ) + U ( x, y ) ( x, y, t )
Or
t
2m0
h2
Lecture 22: Electron Spin
(Shengwang Du, 26&27 April 2011)
1. Introduction
So far, we have learned the non-relativistic Schrodinger equation for a point particle
without any internal degree of freedoms, that is, the time and space cfw_x, y, z, t are all
d
Physics 126
Lecture 21
18 & 20 April 2011
Quantum theory of the Hydrogen Atom
Outline:
Review of 3D central-force problem.
Physical meaning of quantum numbers. Quantization of angular
momentum. Space quantization.
A three dimensional view of the probabili
Lecture 17: The Schrodinger Equation in 1D
Shengwang Du, 4 & 6 April 2011
Review
The time-dependant Schrodinger equation in 1D:
h2 2
ih ( x , t ) =
+ U ( x ) ( x, t )
2
t
2m x
The time-independant Schrodinger equation in 1D (with boundary)
h2 2
E n n