Course Identification

Quantum mechanics 1

Lecturers and Teaching Assistants

Prof. Shimon Levit
Dr. Daniel Kaplan, Tsuf Lichtman, Evyatar Tulipman, Yotam Shapira

Course Schedule and Location

First Semester
Sunday, 11:15 - 13:00, Weissman, Auditorium
Wednesday, 11:15 - 13:00, Weissman, Auditorium

Wednesday, 14:15 - 16:00, Weissman, Auditorium

Field of Study, Course Type and Credit Points

Physical Sciences: Lecture; Obligatory; Regular; 6.00 points
Chemical Sciences: Lecture; Elective; Regular; 6.00 points
Chemical Sciences (Materials Science Track): Lecture; Elective; Regular; 6.00 points


Obligatory for 1st year MSc students
*On November 3rd the lecture will be held at Drori*
*On January 29th the lecture and tutorial will be held at Drori*


Two semesters of undergraduate QM



Language of Instruction


Attendance and participation


Grade Type

Numerical (out of 100)

Grade Breakdown (in %)


Evaluation Type


Scheduled date 1

Weissman Seminar Room A + B

Scheduled date 2

Weissman Seminar Room A + B

Estimated Weekly Independent Workload (in hours)



  1. Motion in external electromagnetic field. Gauge invariance. Symmetries in the presence of gauge fields. The gauge principle - guessing interactions by gauging symmetries. Uniform magnetic field. Electromagnetic field in different gauges. Landau levels.
  2. Quantization of electromagnetic field. Review of the canonical quantization of a field using elastic string as an example. Casting Maxwell equations into canonical Hamiltonian form. Wave functionals. Photons. Number, coherent and squeezed states. Elements of quantum optics. Casimir effect. Interaction with (non relativistic) matter. Multiple expansion. Dipole and higher order transitions. Selection rules. Sum rules.
  3. Second quantization. Review of the many body wave functions for identical particles. Treating Schroedinger equation as a field and its quantization. Equivalence of two approaches. Fock space. Examples of using the second quantization - Hartree-Fock equations for fermions, Gross-Pitaevski equation for bosons. Elementary excitations. Bogoliubov spectrum. Thomas-Fermi method.
  4. The semiclassical approximation. Expansion around stable minima. Multidimensional systems. The WKB approximation. Connection formulae. Bohr-Sommerfeld quantization. Tunneling.
  5. The scattering theory. Scattering amplitude and cross section. The partial wave decomposition, phase shifts. Formal scattering theory - the Lippman-Schwinger equation. The Born approximation. The WKB approximation. Inelastic scatering and reactions.
  6. Time dependent problems and methods of approximation. Adiabatic theory. The Berry phase. Interacting fast and slow systems-the Born-Oppenheimer approach.
  7. Pure and Mixed Systems in Quantum Mechanics. The Density Matrix. Wigner transform.

The learning process is supported and tested by weekly tutorial sessions, homework assignments and final written exam. As a result of studying this course.

* The course’s content might be modified to adjust it  to the audiences’ background

Learning Outcomes

Upon successful completion of this course students should be able to:

  1. Demonstrate good proficiency in topics in advanced quantum mechanics such as the density matrix, physics of decoherence, quantum mechanics of the motion in magnetic field, canonical quantization of simple fields, quantization of EM field and its interaction with non-relativistic matter, second quantization viewed as a quantization of the Schrodinger field and some basic many body phenomena, adiabatic and semiclassical theory.
  2. Continue with further advanced studies of detailed quantum mechanical description of complex atomic, nuclear, quantum optical phenomena as well as basic solid state physics.

Reading List

G. Baym QM, Landau and Lifshits QM, Messiah, QM