Name

1. (16 points) Quantum theory
Under certain circumstances, quantum theory must converge to classical theory.
(a) (6 points) Defme t.~e de Broglie wavelength. Describe the physical properties of
moving objects that would enable detection of their
Phys 3810, Spring 2009
Exam #3
1. If we operate with L+ on Y22 (, ), what do we expect to get? Show that we get this
result.
Since L+ is the raising operator, and there is no state `above'
show this explicitly,
+ i cot
L+ Y22(, ) = he+i
= h
In the second
Phys 3810, Spring 2010
Exam #3
1. What is meant by:
a) SternGerlach experiment
An experiment in which a beam of atoms was separated according to the z component of spin of
the odd electron of the atoms. A nonuniform magnetic field exerted different forc
Phys 3810, Spring 2012
Exam #2
1. Give short denitions of the terms
a) A complete set of eigenfunctions.
This means that any (legal) wave function can be expressed as a linear combination of the eigenfunctions of a certain operator.
b) The spectrum of an
Phys 3810, Spring 2009 Exam #2 1. Give short denitions of the terms (as used by Griths) a) Hilbert space of functions.
This is the set of functions for which the modulus squared can be integrated over the entire applicable space to give a finite result, i
Phys 3810, Spring 2010
Exam #2
1. Give short denitions of the terms (as used by Griths)
a) A complete set of eigenfunctions.
A set of functions with which one can form a linear combination to express any
stats of the system.
other possible
b) Determinate
Phys 3810, Spring 2011
Exam #2
1. Give short denitions of the terms (as used by Griths)
a) A complete set of eigenfunctions.
A set of functions which are eigenfunctions of a certain operator which can be used for an
expansion of any proper wave function
Quantum Mechanics Formulas: by R.L. Grith@ UCB
Physical Constants
Name
Number
Number e
Symbol
e
Eulers constant
Value
3.14159265358979323846
2.71828182845904523536
= lim
Unit
n
n
k=1
Elementary charge
Gravitational constant
Finestructure constant
Speed
Chemistry 160
Integration table
xn eax dx =
0
2
eax dx =
0
0
2
x2n+1 eax dx =
0
1
xm (1 x)n dx =
0
a
sin
0
a
cos
a
n!
2an+1
m!n!
(m + n + 1)!
nx
mx
sin
=
a
a
nx
mx
sin
=0
a
a
x sin2 axdx =
n!
a
cos
0
(1)
an+1
4a
1/2
1 3 5 (2n 1)
2n+1 an
a
2
x2n eax dx =
Chemistry 460
Spring 2013
Dr. Jean M. Standard
March 21, 2013
Linear Variation Method Example: The Morse Oscillator
An illustration of the Linear Variation Method is presented for the Morse oscillator. The Morse oscillator provides a
more realistic model
Electronic Spectroscopy
O2
E =el + G ( ) + F (J )
total
1
E = el + ( + 2 )e + BJ (J + 1)
total
BornOppenheimer approximation separates
electronic and nuclear motion
Selection rules for vibronic transitions:
no restriction on
Electronic Spectroscopy
1
1
Phys 3810, Spring 2011
Exam #3
1. What is meant by:
a) Gyromagnetic ratio (for a particle).
The (constant) ratio of the magnetic moment to the angular momentum for a particle.
b) Larmor precession. Hint: This arose from considering a spin in a uniform B e
Phys 3810, Spring 2012
Exam #3
1. What is meant by:
a) Fermion
Particle of `halfintegral' spin; they must have antisymmetric wave functions (change sign on
exchange of complete coordinates of two particles). The elctron is a famous fermion.
b) Larmor pr
(~
Name
I
2V
1. 0points) Hydrogen atom. The hydrogen atom Hamiltonian can be written as
2;:" :, (r ~ H
2:r
2
2 
4:or E]v ~ 0
+
@(a) Assuming that the wave function can be expressed as If/(r,B,rjJ) = R(r)Yt(B,rjJ)'
derive the equation that governs R(r).
Nowadays climate change is the biggest problem of the human being. It is already
happening and represents one of the greatest environmental, social and economic threats
facing the planet.
The warming of the climate system is unequivocal, as is now evident
[Last Name] 1
Scholastica Kaga Muah
Bartholomaus
English 102
July 6th 2016
Reading Response II
Response to the Immortal Life of Henrietta Lacks
Henrietta Lacks cells have helped improved lives of millions of people, help to develop
polio vaccine (Montagno
Scholastica Kaga Muah
Speech 100
Persuasive speech
To persuade my audience to oppose gun ownership because having guns around the
house creates opportunity for lethal violence, guns create more family tragedies,
guns pose significant risk to children and
Muah1
Scholastica Kaga Muah
Bartholomaus/English 101
March 31, 2016
Essay III
Dysfunctional Justice System
The Criminal justice system in America sometimes seems more criminal than just. It is
filled with error, wrongdoings, racism and cruel, if not unusu
Introduction
Distillation is a laboratory technique used for separating and purifying liquid organic
compounds. Distillation involves selectively volatilizing that is converting from the liquid phase
to the gas phase a component in a mixture. When a compo
Muah 1
Scholastica Kaga Muah
Bartholomaus/English 101
April 19, 2016
Essay IV
What can we do about climate change?
Climate change refers to the changes in earths climatic pattern. These changes pertain to
the issue of temperature, precipitation, or wind w
CHEMISTRY
(AS) cfw_CHEM
010. Academic Based Community ServiceChemistry Outreach. (A)
L/R 012. Environmental Chemistry. (C) Physical World Sector. All classes. The course requires math
literacy at the high school algebra level (2 years) and a willingness
1
Problems and Solutions
Exercises, Problems, and Solutions
Section 1 Exercises, Problems, and Solutions
Review Exercises
1. Transform (using the coordinate system provided below) the following functions
accordingly:
Z
r
Y
X
a. from cartesian to spherical
Roger Grifth
Physics 137B
hw. # 10
Proffessor Clarke
Problem # 1
Consider a single electron in an atom in a high magnetic led so that we can ignore the spinorbit
interaction (PaschenBach effect). We investigate the magnetic dipole transition using the p
Roger Grifth
Physics 137B
hw. # 5
Proffessor Clarke
Problem # 1
Consider a 1D simple harmonic. Use pertubation theory to calculate the shift in the ground state
energy introduce if one uses the relativistic expression (correct to rst order) for the kinet
Rotational Spectra of Polyatomic Molecules
Principle Moments of Inertia
General definition of moment of inertia
I = mi xi2
i
where xi is the perpendicular distance from the axis of rotation (passing
through the center of mass). Rotational properties can b
Roger Grifth
Physics 137B
hw. # 7
Proffessor Clarke
Problem # 1
In an atom with LS coupling, the relative seperations between adjacent energy levels of a particular
multiplet are 4:3:2:1. Assign the quantum numbers s , l , j . Repeat for 7:5:3.
to nd the
Ground state Hatom
Variational Theory
H 0 = E0 0
E0 =
0 *H 0d
E =
0 0d
*
For = 0
2
2
=
H
r
2
2me r r r
(
3
1s = 1 / a0
E 1s
)
1/2
e r /a
0
e
4 0r
2
*H d
*d
E ( , , , . ) E 0
Trial function
(r ) = e r
me e 4
=
2
(4 2 )8 0 2
If an arbitrary
Final solution for Y(,) called
spherical harmonics with
m
Y m ( , ) =( )m ( )
m
Y ( , ) = Nm P (cos )
m
1
e im
1/2
(2 )
m = 0, 1, 2, .,
= 0,1,2, .
2
Y m ( , ) * Yn k ( , ) sin d d = n mk
0 0
L 2 Y m (= ( + 1) Y m ( , )
,)
Lz Y m ( , ) = mY m ( , )
1
1
=
L
sin
sin
2
2
1
+
2
sin
2
2
= i
Lz
L 2 , L = L 2L f L L 2f = 0
z
z
z
Can show mathematically (next slide) that the operators commute.
Implies that we can determine precise values of L2 and Lz simultaneously (or L2 and
Lx or L2 and