MIDTERM TEST PREPARATION ASSIGNMENT
Instructions
Answer all questions Due: 01/10/2016 4:00 pm
1.
Let
2.
Show that every ideal of the ring
3.
integer
Show that
R
be a ring. Show that
( x) y xy and x y xy x, y R
Z
is algebraic over
3
i
2
4.
Solve the equati
Announcements
Quiz 1 available at 4pm (until Mon, Jan 14 at 3pm). If you do
not receive an email later today telling you it is available, you
need to contact me so I can add you to the list.
Yan Hes new office hours are Tues/Thurs 2:00 3:30
Today we ne
AP STaTisTics Name Keg
Normal ApplicaTions using The calculaTor
:1. The SpeedmasTer IV auTomobile geTs an average of 22 miles per gallon in The ciTy. The sTandard deviaTion is
3 miles per gallon. Assume The variable is normally disTribuTed. Find The proba
Assignment:1
Maxwells equations:
1.
2.
Derive expressions for the time averaged energy density for the electric and magnetic
field as well as the time averaged Poynting vector. You will need to start from
conservation of energy in small volume element in
Assignment 4
Polarization and optical activity:
1.
Describe completely the state of polarization of each of the following waves and
write it in the matrix form.
2.
Consider
disturbance
given
by
the
expression
E ( z , t ) = i cos (t ) + j cos t E0 sin (
Assignment 6
Diffraction:
1.
Referring back to the multiple antenna system on p.451 (Hecht), compute the
angular separation between successive lobes or principal maxima and the width of
the central maximum.
2.
A collimated beam of microwaves impinges on a
Assignment 3:
1. The equation for a driven damped oscillator is
m x + m x + m02 x = mqE ( t )
Considering a bound electron as an oscillator,
(a) Explain the significance of each term.
(b) Let E ( t ) = E0 exp ( it ) and the trial solution, x ( t ) = x0 ex
Assignment 5
Scattering, Interference and Coherence:
1.
Work your way through an argument using dimensional analysis to establish the 4
dependence of the percentage of light scattered in Raleigh Scattering.
2.
A white floodlight beam crosses a large volum
Assignment 7
Nonlinear Optics and Ultrafast Optics:
1.
What is the electric field experienced by an electron in a hydrogen atom?
2.
Show that the maximum electric-field intensity, Emax that exists for a given
irradiance I is Emax
I
= 27.4
n
0.5
in units
Assignment 2:
As you drive by an AM radio station, you notice a sign saying that its antenna is 112 m
high. If this height represents one quarter-wavelength of its signal, what is the frequency
of the station?
What is your favorite FM radio stations frequ
Expectation value of the quadrupole operator
The electric quadrupole moment of a nuclear state is defined as the
expectation value of Q op in the substate of maximum M.
Qd JM J Q op JM J
where
Q op e(3 z 2 r 2 )
er 2 (3cos2 1)
16 2
er Y20 ( , )
5
Since
Allowed and Forbidden transitions
The emission of the electron or positron from the nucleus is hindered by
the Coulomb and angular momentum barriers
(similar to the case for the -decay)
Minimum hinderance when
angular momentum for electron/positron
(e ) 0
Hamiltonian:
2
H
V
2
H d Ed d
d a 3 S1 b 3 D1
H11 3S1 H 3S1
Hamiltonian Matrix
H22 3D1 H 3D1
H 11
H
H 21
H 12
H 22
where
H12 H21 3D1 H 3S1
In order to have a non-vanishing off diagonal matrix elements, the
potential V must have a component (Vtens
Ground and excited states of nuclei
A nucleus is a complicated structure of interacting nucleons.
An appropriate quantum mechanical Hamiltonian H can be written
down in terms of nuclear and coulomb interactions.
The Hamiltonian will have a series of eigen
PH 505 Introduction to Nuclear and Particle Physics
Prof. (Mrs.) Pragya Das
Room no. 220 (E), Physics Department
Phone no. 7566 (Ext.)
E-mail: [email protected]
Examinations
Mid-semester
30 marks
Quiz
10 marks
End-semester
50 marks
Class performance 1
Beta-Decay
1) -decay
A(Z, N) A(Z+1, N-1) + e- + e
n p + e- e
2) +-decay
A(Z, N) A(Z-1, N+1) + e+ + e
p n + e+ e
3) Electron-Capture
e - + A(Z, N) A(Z-1, N+1) + e
e- + p n e
Orbital electron is captured by the nucleus.
Free neutron decay:
allowed (mn > mp)
Experimental observations and Independent Particle Model
1) All even-even nuclei have ground state spin parity 0+ (without any
exception).
(i) Since each of the orbit can have (2j+1) particles of one kind, above
experimental observation says that when we
Nuclear Decay
Types of Decay
1) Nucleon-emission or a cluster of nucleon emission (-decay, for
example),
2) -decay,
3) -decay.
Decay can occur spontaneously,
Initiated by bombardment with a particle from outside, called nuclear
reactions.
Conservation
In the shell-model, we include the residual interaction as H.
The energy eigenstates will be the solution of complete Schrdinger
V ' H '
equation
(H0+V) = E -(2)
where is the wavefunction, a state which is the superposition of s.
cii -(3)
i
(This is beca
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Phase space in quantum mechanics an
EP 332(M)
Statistical Physics
Lecture 3: Introduction to
Thermodynamics
Thermodynamics is a funny subject. The
first time you go through it, you don't
understand it at all. The second time you
go through it, you think you understand it,
except for one or
EP 332(M)
Statistical Physics
Lecture 5: The Microcanonical
Ensemble
Microcanonical Ensemble
System
Energy E
Adiabatically isolated
Macrostate M=M(E,x)=M(E,V,N)
The set of corresponding microstates form the
microcanonical ensemble.
Constant Energy Surface
EP 332(M)
Statistical Physics
Lecture 4: Phase Space and
Liouville Theorem
Microstate of a system
Complete specification of system: Positions and
velocities of all particles: 6N coordinates
Quantum mechanical microstate: Wavefunction
Macrostate of a syst