Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
The Wave Function
Problem 1
At time = 0 a particle is represented by the wave function
,
0 ,
(, 0) = , ,
0,
otherwise,
where , , and are constant.
(a) Normalize nd in terms of and .
(Answer: = 3.
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
PHYS 234: Quantum Physics 1 (Fall 2008)
Assignment 8
Issued: November 7, 2008
Due: 12.00pm, November 14, 2008
1. A time dependent two level system
An atom that can exist in one of two energy states (o
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Ehrenfests theorem
The laws of classical mechanics hold for expectation values. This is one sense in
which quantum mechanics can be connected to classical mechanics. This is the content
of
Problem 1.7
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Lecture notes for
ZCT 205
Quantum Mechanics
Yoon Tiem Leong
School of Physics
Universiti Sains Malaysia
Draft last modified on May 31, 2012
Based on the textbook
Introduction to Quantum Mechanics
by D
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
1. Schrdinger equation, wave function, expectation values
A particle of mass m is in the state:
a) For what potential function
First, well plug
b) Does
does
satisfy the Schrdinger equation?
into the S
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
CHAPTER 1
PART I THEORY
THE WAVE FUNCTION
1.1 THE SCHRODINGER EQUATION
Imagine a particle of mass m, constrained to move along the .raxis, subject to
some specied force F (x. t) (Figure 1.1). The pro
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
UNIVERSITETET I OSLO
Det matematisknaturvitenskapelige fakultet
MIDTERM EXAMINATION
Course: Fys 3610 Space Physics
Date: October 8, 2012
Duration: 3 hours
Permitted aid(s): Calculator (with emptied
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Space Physics Lecture Notes
From the Course Rymdfysik I
Anders I. Eriksson
Department of Astronomy and Space Physics
Uppsala University
October 2002
Lightly edited lecture notes on some contents of th
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
PROBLEM 1 (15 points)
In a Cartesian coordinate system, assume the magnetic flux density
where
is a constant,
varies as
( )
is the unit vector in x direction.
a) Sketch the magnetic flux density
and
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
FYS 3610
Exam 2016 Solution
PROBLEM 1 (14 points)
In Magnetohydrodynamics, the equation
of motion is given by
( + ( ) = +
a) Name all variables and give their
units.
b) Using the MHD form of Amperes
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Solution FYS3610 2015
PROBLEM1(10points)
a) Sketchtheentiremagnetosphere,boththedaysideandthenightside.Labelallregions
andboundariesofinterest!(6points)
a. 1ptforcorrectdrawing,bowshock,magnetosheath,
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Magnetospheric Physics  Midterm Exam 3/14/2014
1. Distribution function
Consider a BiMaxwellian distribution function f vk , v = c exp
m2
vk2
kB Tk
+
2
v
kB T
where vk is along
2
the magnetic field
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
The Ehrenfest Theorems
Robert Gilmore
1
Classical Preliminaries
A classical system with n degrees of freedom is described by n second order
ordinary differential equations on the configuration space (
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Ehrenfests Theorem
Lets explore some of the consequences of our result:
d
i
Q =
h
dt
)
) )
Q
H ,Q +
t
[
]
For instance, lets look at the time dependence of the expectation value of the position:
i
d
x
Arizona State University at the Polytechnic Campus
General Physics I
PHYSICS Phys 101

Spring 2012
PHY 101 Lab. Energy Conservation
Purpose
The purpose of this activity is to investigate the relationship between the change in
the gravitational potential energy and the kinetic energy of a falling ob
Arizona State University at the Polytechnic Campus
General Physics I
PHYSICS Phys 101

Spring 2012
PHY 101 Lab. Newtons Laws of Motion
Purpose
The purpose of this activity is to determine what happens to an objects motion (1) when there is no
net force applied to the object; (2) when the mass of th
Arizona State University at the Polytechnic Campus
General Physics I
PHYSICS Phys 101

Spring 2012
Coulombs law states that for a pair of charged objects that are much smaller than the distance between them, the force between them varies directly, as the product of their
charges, and inversely, as
Arizona State University at the Polytechnic Campus
General Physics I
PHYSICS Phys 101

Spring 2012
Coulombs law states that for a pair of charged objects that are much smaller than the distance between them, the force between them varies directly, as the product of their
charges, and inversely, as
Arizona State University at the Polytechnic Campus
General Physics I
PHYSICS Phys 101

Spring 2012
Momentum
a property of moving things
means inertia in motion
more specifically, mass of an
object multiplied by its velocity
in equation form: mass
velocity
(momentum = mv)
A moving boulder has more
Arizona State University at the Polytechnic Campus
General Physics I
PHYSICS Phys 101

Spring 2012
Ice cubes submerged at the bottom of a
liquid indicate that the liquid is less dense
than ice.
When water is turned on in a shower, the
shower curtain moves towards the water. This
has to do with pres
Arizona State University at the Polytechnic Campus
General Physics I
PHYSICS Phys 101

Spring 2012
Coulombs law states that for a pair of charged objects
that are much smaller than the distance between them,
the force between them varies directly, as the product of
their charges, and inversely, as
Arizona State University at the Polytechnic Campus
General Physics I
PHYSICS Phys 101

Spring 2012
The use of inclined planes for
states that the acceleration produced
Galileos experiments helped him to
by a net force on an object is directly
C. discover the property called inertia.
proportional to
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Error Propagation:
Volumes
Abstract:
This lab focuses on finding volumes of different shapes that were presented
along with the idea of determining the correct method of error propagation of the
calcu
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Damped Oscillations
Abstract:
The objective of this lab was to determine the relationship between
amplitude and period of oscillation and finding the damping constant of a simple
swinging pendulum. Th
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Friction: Determination
of and
k
s
Abstract:
Objective:
The objective of this lab was to determine the coefficient of static friction and
the coefficient of kinetic friction of the object dragged acro
Arizona State University at the Polytechnic Campus
Mechanics
PHYSICS 121

Fall 2014
Collisions in One
Dimension
Abstract:
This lab focuses on exploring the idea of collisions in one dimension and the
conservation of kinetic energy and momentum. This was done by performing four
differ
Arizona State University at the Polytechnic Campus
General Physics I
PHYSICS Phys 101

Spring 2012
Chapter 5Energy
MULTIPLE CHOICE
1. The unit of work, joule, is dimensionally the same as:
a.
newton/second.
b.
newton/kilogram.
c.
newtonsecond.
d.
newtonmeter.
ANS: D
PTS: 1
DIF: 1
TOP: 5.1 Work
2.