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
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 w
C104_Summer09_Assignment_1
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
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1. The weight of an object is
a. a measure of
Assignment 2 Summer 09
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
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1. Which of the following would cause a calcium
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. T
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 g
Lecture 3 Notes: Single Slit Experiment
Consequences (II)
x p !
2
x
Heisenberg Uncertainty Principle
Consider diffraction through a single slit
x
D
s
peak-null
distance
l
light,
D
s
l
D l
s
Now cons
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
Lecture 2 Notes: 2-Slit Experiment
sin(kx)
Destructive
interference
=0
sin(kx + )
(out of phase by /2)
This leads to many interference phenomena
Youngs 2-slit experiment
D
l
s
light,
Interference
pat
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
N
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 th
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 t
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
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