PHYC 521: Graduate Quantum Mechanics I


Prof. Alejandro Manjavacas
Office: P&A 21

Teaching assistant
Mr. Anirban Chowdhury


Description of the class

This class corresponds to the first part of a two-semester sequence of classes intended to cover the standard topics of quantum mechanics in a mathematically sophisticated and conceptually rigorous manner. This first part will be centered on the foundations of quantum mechanics, wave mechanics, angular momentum, and central potential problems.


Tuesday and Thursday, 9:30-11:00, P&A Room 184.


We will not be following any text directly. Copies of the lecture note will be available in the web. The are many good texts and I recommend you to pick the one(s) that work best for you. Relevant material from the following recommended texts with be referenced throughout the course.

Recommended texts
Quantum Mechanics, vol I and II by C. Cohen-Tannoudji, B. Diu, and F. Laloė.
Modern Quantum Mechanics by J. J. Sakurai.
Quantum Mechanics by E. Merzbacher.

Other texts
Quantum Mechanics, vol I and II by A. Messiah.
Quantum Mechanics by L. I. Schiff.
Quantum Mechanics, vol I by K. Gottfried.

Office hours

Mondays 3.30-4.30, Tuesdays and Thursdays 11:00-12:00, or by appointment.

Teaching assistant
The teaching assistant is Anirban Chowdhury ( He will be available on Wednesday from 10.00 to 11.30, or by appointment, in room 30 of the P&A building.


The grading in the course will be based on your performance in homework assignments, one midterm exam, and one final exam. The contribution to the final grade is as follows:

  1. Homework: the best (n-1) scores of the n assignments will represent the 30% of the final grade.
  2. Midterm exam: it will represent the 35% of the final grade.
  3. Final exam: it will represent the remaining 35% of the final grade.

The midterm exam is tentatively scheduled for October 10, during class time, and the final exam will be held on December XXX.

Homework assignments

There will be around 10 assignments during the semester each with 4-6 problems apiece. The assignments will be given throughout the semester and will be posted in the tentative schedule about 7-10 before they are due. Late homework policy: homework returned in the next 24 hours after the due dat will be accepted but with 50% penalization. After that no homework will be accepted and the corresponding solutions will be posted here.

I encourage students to study together and learn from each other. However, all homework must be created in its entirety by each student. Evidence of copied homework will result in all involved students being dropped from the class.

Problems class

Listed officially as Phyc 551 (Mondays: 2:00 - 3:00 pm, Room 184). This is a very important adjunct to the main lecture class. It will provide you additional practice with solving problems beyond the homework assignments and self study. Furthermore, the class will also give you a valuable opportunity to bring to my attention your difficulties with any concepts covered in the lecture class so I can address them in a group setting. The problem sheets would be posted here the Friday before the problem class. The corresponding solutions will be posted after the class. You will receive credit for the problems class as long as you register and show up for more than 10 sessions.

Syllabus topics

You can find the calendar for the course in the tentative schedule.

Tentative schedule

Date Subject Homework HW Due Solutions
08/22 (Tu) No class

08/24 (Th)
Introduction of the basic concepts of quantum mechanics.

08/29 (Tu) Mathematical foundations: linear algebra, Dirac notation.
08/31 (Th)
Mathematical foundations: operators, adjoints, change of basis, unitarity.

09/05 (Tu)
no class

09/07 (Th) no class

09/12 (Tu)
Mathematical foundations:  eigenvalues, eigenvectors, commutators. HW2 09/19/17
09/14 (Th)
Structure of quantum mechanics: states and observables.

09/15 (F)
at 12.45 in room 5

Structure of quantum mechanics: measurements.
Stern-Gerlach experiment simulator.

09/19 (Tu) Density operator: pure vs. mixed states. HW3
09/21 (Th) Unitary reversible evolution vs. irreversible stochastic evolution.

09/22 (F)
at 12.45 in room 5
Quantum dynamics: time evolution operator, conservation, and symmetries.

09/26 (Tu) Quantum dynamics 2: Schrödinger picture vs Heisenberg picture.
HW4 10/03/17
09/28 (Th)
10/03 (Tu)
Particle mechanics.

10/05 (Th) Wave mechanics.

10/10 (Tu) Midterm.
Midterm solution.

10/12 (Th) Fall break

10/17 (Tu) Path integrals
Time independent Schrödinger equation: free particle, scattering states, constant potentials.
10/19 (Th)
Time independent Schrödinger equation: parity, bound states.

10/24 (Tu) Simple harmonic oscillator (SHO): review classical problem, creation/annihilation operators, eigenstates.

10/26 (Th) Simple harmonic oscillator (SHO): x-p space, uncertainty relations, position/momentum, number/phase. HW6
10/31 (Tu) Simple harmonic oscillator (SHO): coherent States, phase space, and the classical liimit.

11/02 (Th) Multiple degrees of freedom 1. HW7
11/07 (Tu) Multiple degrees of freedom 2.

11/09 (Th) Solving the Schrödinger equation with multiple degrees of freedom

11/14 (Tu) Angular momentum algebra. HW8
11/16 (Th)
at 8.30
Oribtal angular momentum and spherical harmonics.

11/21 (Tu) Central potentials and the radial equation.

11/23 (Th) Thanksgiving

11/28 (Tu) No class
11/30 (Th) Radial equation continued: partial waves.

12/01 (F)
at 12:45 in room 5
Radial equation continued: spherical wells.

12/05 (Tu) Spin-1/2: Pauli algebra.

12/07 (Th) Questions and doubts. Casimir effect.

12/12 (Tu)
Final exam

Problems class

Date Problems Solutions
No class

Problems class 1
Problems class 1
Labor day

Problems class 2 Problems class 2
Problems class 3 Problems class 3
Problems class 4 Problems class 4
Problems class 5
Problems class 5
Problems class 6 Problems class 6
Problems class 7 Problems class 7
Problems class 8 Problems class 8
Problems class 9 Problems class 9
Problems class 10 Problems class 10
Problems class 11 Problems class 11
Problems class 12 Problems class 12
Problems class 13 Problems class 13
Problems class 14 Problems class 14

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