Central Forces Homework 2
Due 03/02/12
REQUIRED:
1. Consider a very light particle of mass scattering from a very heavy, stationary particle
of mass M . The force between the two particles is a repulsive Coulomb force rk2 . The
impact parameter b in a sca
Central Forces
Conic Sections
Complete and keep in your notebook
In the Mathematica worksheet, http:/physics.oregonstate.edu/ph426/mathematica/cfconics.nb, you
will examine a two parameter family of curves described by the polar equation
r() =
1 + cos()
D
Central Forces
Effective Potentials
Keep in your notebook
In the Mathematica worksheet, http:/physics.oregonstate.edu/ph426/mathematica/cfeffpotential.nb,
you will be examining how various parameters affect the shape of the effective potential. Experiment
Central Forces
Orbits
Keep in your notebook
In the Mathematica worksheet, http:/physics.oregonstate.edu/ph426/mathematica/cforbits.nb, you
will be examining how various parameters affect orbits.
1. Work through the worksheet until you have plotted the eff
Central Forces Homework 1
Due 2/29/12
PRACTICE:
1. If a central force is the only force acting on a system of two masses (i.e. no external
forces), what will the motion of the center of mass be?
2. Which of the following forces can be central forces? whic
Central Forces
Velocity and Acceleration in Polar Coordinates
1. Find r and in terms of r and .
2. Find ~v and ~a in terms of r and .
Corinne Manogue
c
1999
Corinne A. Manogue
Central Forces Homework 3
Due 03/07/12
REQUIRED:
1. NASA has launched a satellite into a circular orbit around the earth and wants to
increase the radius slightly while maintaining a circular orbit. NASA scientists propose
to fire the engines briefly, app
Central Forces Homework 5
Due 03/14/12
PRACTICE:
1. (McIntyre 7.20)
In each of the following sums, shift the index n n + 2. Dont forget to shift the
limits of the sum as well. Then write out all of the terms in the sum (if the sum has
a finite number of t
Central Forces Homework 6
Due 03/16/12
PRACTICE:
1. (McIntyre 8.2) Use the recurrence relation for the radial wave function to construct the
n = 3 radial states of hydrogen. Calculate the normalization constant for the R32 (r)
state.
2. (McIntyre 8.5) By
Central Forces
Corinne A. Manogue
with Tevian Dray, Kenneth S. Krane, Jason Janesky
Department of Physics
Oregon State University
Corvallis, OR 97331, USA
corinne@physics.oregonstate.edu
c
!2007
Corinne Manogue
March 1999, last revised February 2009
Abstr
Quantum Calculations on a Ring I
Before you begin, recall that an arbitrary state |i can be written as
.
.
.
.
h4|i
a
4
h3|i a3
h2|i
a
2
h1|i a1
.
= a0
h0|i
|i =
h1|i
a
1
h2|i a2
h3|i
a
3
h4|i
a4
.
.
.
.
In this activity,
Central Forces Homework 4
Due 03/09/12
PRACTICE:
1. (McIntyre 7.5)
An angular momentum system with l = 1 is prepared in the state:
2
3
4
| = |1, 1 + i |1, 0 |1, 1
29
29
29
(a) What are the possible results of a measurement of the angular momentum componen
Quantum Calculations on a Ring II
In this activity, your group will carry out calculations on the following quantum state on a ring:
|i =
3
4
| 1i + |2i
5
5
1. You carry out a measurement to determine the energy of the particle at time t = I
6
h . Calcula