MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Department of Physics
Physics 8.01 TEAL
Fall Term 2004
In-Class Problems 23-24: Harmonic Oscillation and Mechanical
Energy: Solution
Problem 22: Journey to the Center of the Earth
Imagine that one drilled a hole with
Problem Set 9
8.04 Spring 2013
Solutions
Thursday, May 2
Problem 1. (10 points) Coulomb Potential Superposition States
(a) (2 points) Our wavefunction is given by
= C 100 + 4i
p
2 2
210
22 1
(1)
To normalize, we compute ( | ) and set it to 1:
Z 1Z 1Z 1
p
Problem Set 8
8.04 Spring 2013
Solutions
April 17, 2013
Problem 1. (15 points) Superposition State of a Free Particle in 3D
(a) (4 points) Recall from lecture that the energy eigenstates of a free particle in 3D are
given by
h
i
= A exp i ~ ~ = A exp [i
2-68: Let h be the height of the window, At time the owerpot takes
to pass the window and d the distance between the windowsill where the
owerpot started and the top of the window below. (using a coordinate
System where a: points downwards and the owerpot
8.04: Quantum Mechanics
Massachusetts Institute of Technology
Professor Allan Adams
Wednesday April 10, 2013
Problem Set 8
Due Wednesday April 17, 2013 at 10.00AM
Assigned Reading:
E&R
Li.
Ga.
Sh.
7all , AppM,N
86 , 91,2,3 , 101,2,3
7all , 81,4,5
12all
1.
8.04: Quantum Mechanics
Massachusetts Institute of Technology
Professor Allan Adams
Thursday April 25
Problem Set 9
Due Thursday May 2 at 11.00AM
Assigned Reading:
E&R
Li.
Ga.
Sh.
7all , AppM,N
82,3 , 10all
4c , 8all
13all
1. (10 points) Coulomb Potential
Problem 1: (Experiment AM)
In experiment AM, a circular steel washer, of mass m1 and moment of inertia I =
4.0 x 10-5 l<gm2 , is mounted on the shaft of a small motor. Assume that the
moment of inertia of the motor is negligible. The washer is set into mo