Animation of an excited state of Hydrogen, by Drexel student Glenn Winship.
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Course Description and Philosophy
Course Outline
Textbook and Reading Assignments
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Problem Set Solutions
Problem Hints
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Course Schedule
Miscellaneous
Solutions to the final exam are posted below.
Welcome to the home page of QM II. This is your resource page for information about the course, including homework assignments, exams, and solutions. This web page is also the syllabus for the course. To save paper, I will not print and distribute copies of documents in class. You may read them on the web or your computer and print out if you need.
In this second quarter of our three part sequence on QM, we'll move on to three dimensional problems, and the QM description of the Hydrogen atom, from which you could first see how the QM formulation yields accurate predictions of the observed phenomena, and begin study of multi-particle systems and perturbation theory.
See the course outline above for the chapters that correspond to the material covered in this course.
I will also hand out photocopies of selected passages from other QM texts, as necessary to supplement Griffiths.
You may discuss the homework with your classmates, but you and you alone are responsible for the work that you turn in. Please write up your own solutions to the problems. Breaches of this policy will result in homework scores being divided by the number of ``participants.'' Second offenses may result in failure (of the class).
Use of solutions to these problems from previous years or any other source constitutes plagiarism. You must attribute (by giving the correct reference) any significant help that you receive from outside sources.
Problem Set 1 (Due Thursday, January 17):
Griffiths 4.3, 4.8, 4.9, 4.38 and the following:
Find the l=0 energy and total wave function (radial and angular parts together and properly normalized) of a particle of mass m that is
subject to the central potential V(r)=0 in the region from r=a to r=b and
V=infinity elsewhere (below r=a and above r=b), thus the particle is
trapped in a cavity between two hard spheres.
Problem Set 2 (Due Thursday, January 24):
Griffiths 4.11, 4.13, 4.17, and the following:
(a) For the following cases, calculate the value of r at which the radial probability density of the hydrogen atom reaches its maximum: (i) n=1, l=0, m=0 (ii) n=2, l=1, m=0 (iii) l=n-1, m=0
(b) Compare the values obtained with the Bohr radius for circular orbits.
Problem Set 3 (Due Thursday, January 31):
Griffiths 4.18, 4.22, 4.27, 4.28, 4.57
Problem Set 4 (Due Thursday, February 7):
Griffiths 4.34, 4.49, 4.52, 4.55 and the following:
For a particle with spin s=1/2, find the eigenvectors and eigenvalues of the operator S_x + S_y.
Problem Set 5 (Due Thursday, February 21):
Griffiths 5.4, 5.5, 5.6 and two problems in the following PDF document:
Problem Set 5 assignment (PDF)
Problem Set 6 (Due Thursday, February 28):
Griffiths 5.7, 5.33, and three more problems in the following PDF document:
Problem Set 6 assignment (PDF)
Problem Set 7 (Due Thursday, March 6):
Griffiths 5.16, 5.17, 5.34, 5.35 (see Homework Hints below re problem 5.35).
Problem Set 8 (Due Thursday, March 13):
Griffiths 5.22, 5.23, 5.24, 5.30
Problem set 7, 5.35: In (a) use Eq. 5.45 to write the total energy in terms of N, q, and m. In part (b) you can compute the total (negative!) gravitational energy of a uniform sphere by considering how much work must be done to add an amount of mass m to the star (this work is negative) and then integrating. You should get E=-(16 \pi^2 \rho^2 R^5 G/15) where \rho is the density of the star. In part (c), add up the two energy terms and find the minimum by taking the derivative (duh). Then plug in all the numbers and check that you get the given answer. In part (d), the mass of the Sun is 1.989 X 10^{30} kg. In part (e), there are 1.602 X 10^{-19} Joules/eV. The rest energy of an electron is 0.511 MeV (memorize this!).
The final exam will be held during the usual exam week.
Both exams will be half closed and half open book.
| Week | Class Dates | Reading | Homework | Exams |
| 1 | January 8, 10 | 4.1 | ||
| 2 | January 15, 17 | 4.2 | HW1 | |
| 3 | January 22, 24 | 4.3, 4.4 | HW2 | |
| 4 | January 29, 31 | 4.4 | HW3 | |
| 5 | February 5, 7 | 5.1, 5.2 | HW4 | |
| 6 | February 12, 14 | 5.2, 5.3 | Midterm in class 2/12 | |
| 7 | February 19, 21 | 5.4 | HW5 | |
| 8 | February 26, 28 | 6.1, 6.2 | HW6 | |
| 9 | March 4, 6 | 6.2, 6.3 | HW7 | |
| 10 | March 11, 13 | 6.3, 6.4 | HW8 | |
| 11 | No Class | Final Exam, TBA |
Last update: March 24, 2008