Lecture 7 Notes: Fixed Distances
Consider the rotation of two particles at a fixed distance R from one another:
r r R
1
2
m1
m1r1 m2 r2center of mass (COM)
r1
r2
COM
m2
These two particles could be an electron and a proton (in which case wed be
looking at
5
Multiple Choice
Identify the choice that best compietes the statement or answers the question. (10 points each)
1. What is the final concentration of a NaCi solution prepared by adding 20.0 m l of water to 30.0 m l of 5.00 M
solution?
,
M
b.
c

3 33 M
C104_Summer09_Assignment_1
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
_
_
_
_
_
_
_
_
_
1. The weight of an object is
a. a measure of the gravitational force pulling the object toward the e
Assignment 2 Summer 09
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
_
_
_
_
_
_
_
_
_
_
1. Which of the following would cause a calcium atom (Ca) to achieve a noble gas configuration?
a. lose
Lecture 1 Notes: Atom Structure
Niels Bohr, a Danish physicist who established the Copenhagen school.
(a) Assumptions underlying the Bohr atom
(1)
Atoms can exist in stable states without radiating. The states have
discrete energies En, n = 1, 2, 3,., whe
Lecture 4 Notes: Boundary Conditions
Free particle and the particle in a box
nd
Schrdinger equation is a 2 order diff. eq.
!22 x
V x x E
x2mx2
We can find two independent solutions 1 x and 2 x
The general solution is a linear combination
x A1 x B2x
A a
Lecture 3 Notes: Single Slit Experiment
Consequences (II)
x p !
2
x
Heisenberg Uncertainty Principle
Consider diffraction through a single slit
x
D
s
peaknull
distance
l
light,
D
s
l
D l
s
Now consider a beam of electrons with de Broglie wavelength . T
Lecture 6 Notes: Order Commutators
Order counts when applying multiple operators!
e.g.
A px= ?
and can we write px xp
?
operate on function to obtain .
Af
x g x
i!x d
dx
f x i!f
px f x
x i!x
d
i!
x f x
dx
d i! f x
dx
d
i!x
A
i! px
dx
Now try B xp
d
B
Lecture 2 Notes: 2Slit Experiment
sin(kx)
Destructive
interference
=0
sin(kx + )
(out of phase by /2)
This leads to many interference phenomena
Youngs 2slit experiment
D
l
s
light,
Interference
pattern
observed
screen
D
s
l
D
l
s
Light as a particle
Lecture 5 Notes: Average Deviation
xi x
th
xi x
Deviation of i
Average deviation from average value <x>
xi x
But for particle in a box,
xi x 2
0
Square of deviation of i
value <x>
xi x 2
x
2
xi x 2
Note
measurement from average value <x>
th
measurement f
Lecture 8 Notes: Hamiltonian Products
Hx
Schrdingers Eq. becomes:
H
x
Then try solution of form
Hy
Hz
x, y, z
H y H z x, y, z E
x , y , z x y z
x y z
(separation of variables)
Where we assume that the 1D functions satisfy the appropriate 1D TISE:
H
2
Lecture 9 Notes: Algebraic Skills
Since L and Lz commute, they share common eigenfunctions. These functions are
extremely important for the description of angular momentum problems they
determine the allowed values of angular momentum and, for systems
Lecture 10 Notes: Spacing
m
Yl
Y ,l
m
l 0, 1, 2,.
,lmm
2l 1 l m !
4 l m !
m
Y
1
m
Pl
0
5
3
Y
1
2
1
2
16
1
0
3cos2 1
1
cos
15 2
Y1
2
4
3
1
2
i
sin cose
8
1
1
Y
im
H Efor the rigid rotor problem.
Y2
4 1 2
0
cose
2
m 0,1, 2, 3,. l
Yl s are the eigenfunct
The Nano Text Editor
Introduction
Nano is a text editor suited to working in UNIX. It is not as powerful as PC windowbased
editors, as it does not rely on the mouse, but still has many useful features.
Most nano commands are invoked by holding down the C