(Sommersemester): Quantum Mechanics (Theory) - Integrated course 1 (IK-1)

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  • Lecturer: Andrea Aiello
  • Contact: Andrea Aiello
  • Lectures: Monday 13:30 - 15:30, SR 01.683; Tuesday and Thursday, 10:00 - 12:00, SR 01.683; Wednesday 11:00 - 13:00, SR 01.683
  • Exercises: Thursday 13:00 - 16:00, SR 00.103
  • 8 hours/week, 8 ECTS credit points

Preliminary program

Lecture notes

Exercise sheets


  • From p. 414 of: Peter D. Lax, Functional analysis, (John Wiley & Sons, Inc., 2002)

The theory of self-adjoint operator was created by von Neumann to fashion a framework for quantum mechanics. [...] I recall in the summer of 1951 the excitement and elation of von Neumann when he learned that Kato has proved the self-adjointness of the Schroedinger operator associated with the helium atom. And what do the physicists think of these matters? In the 1960s Friedrichs met Heisenberg, and used the occasion to express to him the deep gratitude of the community of mathematicians for having created quantum mechanics, which gave birth to the beautiful theory of operators in Hilbert space. Heisenberg allowed that this was so; Friedrichs then added that the mathematicians have, in some measure, returned the favor. Heisenberg looked noncommittal, so Friedrichs pointed out that it was a mathematician, von Neumann, who clarified the difference between a self-adjoint operator and one that is merely symmetric."What's the difference", said Heisenberg.

  • From p. vii of: Josef M. Jauch, Foundations of Quantum Mechanics, (Addison-Wesley Publishing Company, Inc., 1968)

Contrary to a widespread belief, mathematical rigor, appropriately applied, does not necessarily introduce complications. In physics it means that we replace a traditional and often antiquated language by a precise but necessarily abstract mathematical language, with the result that many physically important notions formerly shrouded in a fog of words become crystal clear and of surprising simplicity.

  • From p. vii-viii of: Cornelius Lanczos, The variational principles of mechanics, 4th ed. (Dover Publications, Inc., 1970)

Many of the scientific treatises of today are formulated in a half-mystical language, as though to impress the reader with the uncomfortable feeling that he is in the permanent presence of a superman.


  • R. Shankar, Principles of Quantum Mechanics, 2nd ed. (Springer, 1994) - basic
  • R. L. Liboff, Introductory Quantum Mechanics, (Addison-Wesley, 1980) - basic
  • S. Gasiorowicz, Quantum Physics, 3rd ed. (John Wiley & Sons, 2003) - basic
  • D. J. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (Cambridge University Press, 2016) - basic
  • E. Merzbacher, Quantum Mechanics, 3rd ed. (John Wiley & Sons, 1998) - intermediate
  • J. J. Sakurai, Modern Quantum Mechanics, 3rd ed. (The Benjamin/Cummings Publishing Company, Inc., 1985) - intermediate
  • W. Greiner, Quantum Mechanics, An Introduction, 4th ed. (Springer-Verlag, 2001)- intermediate
  • C. Cohen-Tannoudji, B. Diu, F. Lalöe, Quantum Mechanics, Vol. I and Vol. II (John Wiley & Sons, 2005) - intermediate/advanced
  • G. Baym, Lectures on Quantum Mechanics, (Westview Press, 1990) - intermediate/advanced
  • L. D. Landau, L. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory (Volume 3), 3rd ed. (Butterworth-Heinemann, 1981) - intermediate/advanced
  • A. Messiah, Quantum Mechanics, (Dover Publications, Inc., 1999) - intermediate/advanced
  • S. Weinberg, Lectures on Quantum Mechanics, 1st ed. (Cambridge University Press, 2013) - intermediate/advanced
  • J. Schwinger, Quantum Mechanics, (Springer, 2001) - advanced
  • A. Galindo, P. Pascual, Quantum Mechanics I and II, (Springer, 1990) - advanced
  • A. Peres, Quantum Theory: Concepts and methods, (Kluver Academic Publishers, 1995) - advanced
  • A. Sudbery, Quantum mechanics and the particles of nature, 3rd ed. (Cambridge University Press, 1986) - alternative
  • T. F. Jordan, Quantum mechanics in simple matrix form, (Dover Publications, Inc., 1986) - alternative
  • T. F. Jordan, Linear Operators for Quantum Mechanics, (Dover Publications, Inc., 1997) - mathematics/mathematical physics
  • C. Lanczos, Linear Differential Operators, (Martino Publishing, 2012) - mathematics/mathematical physics
  • I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic Press, 1994) - mathematics/mathematical physics
  • A. Papoulis, S. U. Pillai, Probability, Random Variables and Stochastic Processes, 4th ed. (McGraw-Hill, 2002) - probability theory
  • J. M. Jauch, Are Quanta Real? (Indiana University Press, 1989) - didactic/history
  • G. Gamow, Thirty years that shook physics. The story of quantum theory, (Dover Publications, Inc., 1985) - didactic/history

Online resources

Relevant didactic articles

  • On quantum theory, Eur. Phys. J. D (2013) 67: 238 One of the most lucid and scientifically honest recent expositions of quantum theory by B-G. Englert, one of the last PhD students of Julian Schwinger. Some of the so-called paradoxes of quantum mechanics are analyzed and deconstructed.
  • What is a state vector? American Journal of Physics 52, 644 (1984) This and the next article are from the late Asher Peres, one of the most profound modern thinkers about quantum mechanics (see his celebrated book above). In this article Peres shows that "[...] a state vector represents a procedure for preparing or testing one or more physical systems. No "quantum paradoxes" ever appear in this interpretation."

Material for exercises

  • Quantum Physics I - exercises Quantum Physics I, Allan Adams, Matthew Evans, and Barton Zwiebach. 8.04 Quantum Physics I. Spring 2013. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.