Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 4  Solutions
Prof. J. Gerton
September 16, 2011
Problem 1
(10 pts.) Solar fusion
In the reaction, it takes four protons and two electrons to form a Helium4 nucleus
at rest. In the process, the missing mass energy can be found as e
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
HW5 (3740 Fall 2016)
Due Tuesday 11/08/2016 during the class.
1) Probabilistic interpretation of wave functions
A particle moving in one dimension between rigid walls separated by a distance 2L
has, in its ground state, the wave function () = sin( 2 ) . T
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
HW3 (3740 Fall 2016)
Due Friday 09/30/2016 during the class.
1) The work function for lithium is 2.9eV.
a) What is the photoelectric effect threshold frequency and wavelength
b) What is the stopping potential when the wavelength of the light is 100 nm?
2)
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
HW 1 (3740 Fall 2016)
Due Friday 09/02/2016 during the discussion session.
1) A shift of one fringe in the MichelsonMorley experiment would result from a difference of
one wavelength or a change of one period of vibration in the roundtrip travel of the
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
HW4 (3740 Fall 2016)
Due Wednesday 10/18/2016.
1) Classical uncertainty relation
A phone line is capable of transmitting over a range of frequencies f =3000Hz .
What is the duration of the shortest pulse that can be transmitted over the line?
2) In one of
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
HW2. Due Wednesday September 14th in class or by email before the midnight (09142015 11:59PM) to both [email protected] & [email protected]
1. A particle is moving at such a speed that it can travel from the Europa to Jupiter in 5
s. (a)A
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Problem Set 12  Solutions
Prof. J. Gerton
December 12, 2011
Problem 1
(10 pts.) Recoil of a nucleus
The total energy of the photon equals the energy dierence between the two levels,
E=
2 me c2
1
1
(1 2 ) = 13.6 eV (1 2 ).
2
n
n
(1)
The momentum of such p
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 8  Solutions
Prof. J. Gerton
October 24, 2011
Problem 1
(10 pts.) Solving a PDE
We write (x, t) = f (x)g (t), so that we can separate the equation in an xdependent
and a tdependent part as
f (x)
= (A + ex )f (x),
x
(1)
and
g (t)
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 9  Solutions
Prof. J. Gerton
October 23, 2011
Problem 1
(10 pts.) The quantum harmonic oscillator
(a) The Schroedinger equation for the ground state of the 1D QHO is
2
2
m 2 x2
+
2m x2
2
(x) = E0 (x).
(1)
2
2
(x) =
B (1 2B x2 ) (
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 10  Solutions
Prof. J. Gerton
November 27, 2011
Problem 1
(10 pts.) Raising/lowering operators
(a) We dene
m 1/4
m
,
,
2
so that the wave function for the ground state of the QHO is rewritten as
A
2
0 (x) = A e x .
(1)
(2)
From th
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Problem Set 11  Solutions
Prof. J. Gerton
December 1, 2011
Problem 1
(20 pts.) Scanning tunneling microscope
(a) Using the conservation of energy E = p2 /2me + V0 , we obtain the momentum
p=
2me (E V0 ).
(1)
2me E V0 .
(2)
Now, since V0 > E , we write
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 7  Solutions
Prof. J. Gerton
October 24, 2011
Problem 1
(10 pts.) Quantization of the Bohr model
In Bohrs model , the velocity of the electron is quantized as vn = c/n, where
= 1/137 is the ne structure constant. Since c = 2.19 10
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 6  Solutions
Prof. J. Gerton
October 17, 2011
Problem 1
(10 pts.) DavissonGermer experiment
(a) Electrons acquire a kinetic energy K = V0 . Since this kinetic energy is K
me c2 ,
nonrelativistic mechanics can be used. The momentu
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 1  Solutions
Prof. J. Gerton
August 30, 2010
Problem 1
(10 pts.) If aether existed.
In the frame of the aether, the speed of light is c, and the motorcycle moves with
respect to aether with velocity v . We associate to the aether t
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 2  Solutions
Prof. J. Gerton
September 7, 2010
Problem 1
(10 pts.) Consequences of Special Relativity
(a) We use the time dilation rule
t = t.
(1)
If we want the clock to run at twice the pace compared to the rest frame, we need
=
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 3  Solutions
Prof. J. Gerton
September 14, 2011
Problem 1 (10 pts.) Relativistic expression for the momentum and
kinetic energy
(a) The relativistic expression for the kinetic energy is
1
K = E mc2 = ( 1) mc2 =
Using a Taylor expan
Introduction to Relativity & Quantum Mechanics (Modern Physics)
PHYS 3740

Fall 2013
Relativity Problem Set 5  Solutions
Prof. J. Gerton
October 8, 2011
Problem 1
(10 pts.) Wavelengths
(a) The electron has kinetic energy K = 10 MeV
me c2 , so it is ultrarelativistic
and pc E = 10.511 MeV. Its wavelength is thus
e =
h
hc
.
p
E
(1)
Since