Intermediate Quantum Mechanics
Spring 2017
Homework 5
1) An electron in the state of spin-up in the x-direction | i is placed in a region with a
uniform magnetic field, B, in the z-direction. After a
Intermediate Quantum Mechanics
Spring 2017
Solutions to Homework 8
1) Calculate the following commutators:
x, L
y]
[L
+, L
z]
[L
z]
[L2 , L
, L
z]
[L
+, L
]
[L
Solution
x = ypz zpy
L
y = zpx xp
Intermediate Quantum Mechanics
Spring 2017
Solutions to Homework 3
1) Show that the vector specifying the state of an electron that is spin up in the n
direction is given by:
!
cos 2
|n i =
sin 2
wher
Intermediate Quantum Mechanics
Solutions to Homework 4
1) A particle is in the state |i with probability distribution in x given by the Gaussian:
1/2
1
2
2
(x)(x) =
ex /2x
2
2x
where (x) is the repre
Intermediate Quantum Mechanics
Spring 2017
Homework 6
1) If the initial wave packet has a small enough , then we can have:
1
(t)
=
4
h
m
> c
This would seem to violate relativity since initially the p
Intermediate Quantum Mechanics
Spring 2016
Solutions Homework 8
1) In class we discussed expressions for the ground state energy and the Bohr radius of the
hydrogen atom in terms of the constants: h
Intermediate Quantum Mechanics
Spring 2017
Solutions to Homework 1
1) For the following objects at room temperature, T 300 K, determine the approximate
distance scale at which effects due to quantum m
Intermediate Quantum Mechanics
Spring 2016
Solutions to Homework 2
1) Prove that the trace of an operator, the sum of the diagonal elements of the matrix,
is independent of the basis chosen to represe
Intermediate Quantum Mechanics
Spring 2017
Solutions Homework 10
1) For the spin system of two electrons we have for the total angular momentum:
Jz = S1z + S2z
J2 =
J+ = S1+ + S2+
J = S1 + S2
S1 + S2
Intermediate Quantum Mechanics
Spring 2017
Solutions Homework 7
a
a
1) Evaluate the commutation relations [H,
] and [H,
].
Solution
a
[H,
] = [(
h
a a
+h
/2), a
] = h
[
a a
, a
] = h
(
a a
a
a
19. If the potential energy of a particle is given by U = x2 - 4xy, find the
magnitude and direction of the force on the particle when it is located at the
point (2, 5).
0 Please explain your reasoning clearly - it is your responsibility to convince me that you
understand the material.
- Points will be deducted for incorrect and/or incomplete reasoning, or for evidenc
0 Please explain your reasoning clearly it is your responsibility to convince me that you
understand the material.
0 Points will be deducted for incorrect and/or incomplete reasoning, or for evidence
A constant force F is applied to the wheel shown below through the rope. The wheel
rolls without slipping on the horizontal surface [which is not possible without
friction). The wheel has a mass M, ra
- Please show all work
. Please box your nal answers
0 Points will be deducted for incorrect working or misconceptions even if
nal answer is correct
A solid sphere of radius r and mass In (rotational
0 Please explain your reasoning clearly it is your responsibility to
convince me that you understand the material.
. Points will be deducted for incorrect and / or incomplete reasoning, or
for evidenc
Exam
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
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2015 Final Exam
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
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Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
^
^
1) Object A has a position as a function of time given by r A(t) = (3.00 m/s)t i +
Exam
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) In the figure, point P is at rest when it is on the x-axis. The linear speed of poi
Test 2
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) In order to get an object moving, you must push harder on it than it pushes back
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Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) The acceleration of an object as a function of time is given by a(t) = (3.00 m/s3 )
Exam
Name_
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
1) A uniform solid sphere is rolling without slipping along a horizontal surface with