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September 16, 2013
Limit of classical mechanics, need for quantum mechanics.
We discuss the physics early 20th century when the limit of classical was rst noticed and the
new quantum mechanics was born.
I.
A.
PHOTONS
Einsteins photon
It was Albert Einstei
November 4, 2013
Particle states in a central potential in 3D
The central force with V (r) is considered. Some typical technics to solve such problem is developed
and then applied to Hydrogen atom and 3D SHO.
I.
A TWO BODY PROBLEM
We are interested in a t
December 9, 2013
Symmetries in Quantum mechanics
A symmetry principle is a statement that, when we change our point of view in certain ways, the
laws of nature do not change. In quantum mechanics, symmetry transformations must not change
transition probab
September 26, 2013
1D problems of QM
Some problems in 1D QM are solved.
Lets get started from a famous story of two gures in quantum mechanics: Dirac and Feynman. Paul Dirac was
notoriously a man of few words. Dick Feynman told the story that when he rst
September 30, 2013
Path integral formulation of QM
Hamiltonian formulation of classical mechanics provided the version of quantum mechanics we
have learned so far (canonical formulation based on Dirac brackets). In this lecture, we will describe
Lagrangia
September 23, 2013
General principles of Quantum Mechanics
This lecture will describe the principles of quantum mechanics in a formalism which is essentially
the transformation theory of Dirac.
There is no proof for quantum mechanics. What we can say is t
September 9, 2013
Lagrangian, Hamiltonian formalism of classical mechanics
We review basic ideas of Newtonian, Lagrangian and Hamiltonian mechanics.
I.
NEWTONIAN MECHANICS
A particle of mass m with an external force F is subject to follow the Newtons equa
Quantum Mechanics Homework # 3 : solution
(Due : October 14, 2013)
Lecture note # 2
Homework # 5
Write Schrdinger equation for simple harmonic oscillator in 3D with a potential V =
o
1
2 2
m x .
2
Solution :
The Schrdinger equation is i
o
t
= H. The Hami
Quantum Mechanics Homework # 1 : solution
(Due : September 23, 2013)
Lecture note # 1
Homework # 1
With the conservative force, the energy, E = 1 mx2 + V (x), is constant of time, i.e. dE/dt =
2
0.
Solution :
Conservative force can represented by potenti
Quantum Mechanics Homework # 2 : solution
(Due : September 30, 2013)
Lecture note # 2
Homework # 1
Derive = + e (1 cos ) for the Compton scattering with initial (nal) photons wave
length ( ) and the scattering angle . The length e = h/(me c) = 2.425 1010
Homework 2, due January 29, 1999
Problem 1. AshcroftMermin 5.2
dl=a3,a2:%c+ afg753202
#2 X 43 = %3+ cg/git
*3 x [1 = acg
51 X #2 = [g/32A
(7:1 X 62 #3 = (Ra
31 = 2%(90 r?) f3:e)+ 27; 35:
52 2 47:32)
332279
The angle between the rst two vector
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PHYS 635 Solid State Physics Take home exam 1
Gregory Eremeev Fall 2004 Submitted: November 8, 2004
Problem 1:Ashcroft & Mermin, Ch.10, p.189, prob.2 a) Lets prove xx = yy = zz = xx = = Now 0 = xx yy = dr (x2 y 2 ) (r)2 U (r) (3) dr (r) x (r) U (r) = x
Problem A& M 6.1 First make sure you understand Equation 6.12 in A&M (pp 103104). It shows that the planes corresponding to the smallest reciprocal lattice vector yield the smallest angle for the ring. Thus we know that the angle at which the j th diract
Homework 6, due December 6, 1996
Problem 1 Part a) At x ? a (x) = AeiK x + (Ar + B t)e?iKx 2 At x a (x) = (At + Br)eiKx + Be?iKx a 2 2 From (8.68) ( a ) = eika (? a ) a= eika(Ae?aiK 2 + (Ar + Bt)eiK a ) 2 2 which is equal to (At + Br)eiK 2 + Be?iK 2 which
PHYSICS 880.06 (Fall 2004)
Problem Set 3 Solution
3.1
A&M Chapter 4 Problem 1
(a)
Basecentered cubic: is a Bravais lattice, with a set of three primitive vectors that can be chosen as
a1 =
a
( y),
x
2
a2 =
a
( + y),
x
2
a3 = az,
where a is the length of
PHY 140A: Solid State Physics
Solution to Homework #3
TA: Xun Jia1
October 23, 2006
1 Email:
jiaxun@physics.ucla.edu
Fall 2006
c Xun Jia (October 23, 2006)
Physics 140A
Problem #1
(a). Show that the structure factor for a monatomic hexagonal closepacked
PHY 140A: Solid State Physics
Solution to Homework #2
TA: Xun Jia1
October 14, 2006
1 Email:
jiaxun@physics.ucla.edu
Fall 2006
c Xun Jia (October 14, 2006)
Physics 140A
Problem #1
Prove that the reciprocal lattice for the reciprocal lattice is the origina
PHZ 5941
Condensed Matter I
Problem Set 5 Solution
5.1 Problem 6.3, A&M, Pg. 109
(a) The HCP structure is described as a simple hexagonal Bravais lattice with a two point
basis. The primitive vectors of the simple hexagonal lattice can be taken to be thos