(Sommersemester): Quantum Mechanics (Theory) - Integrated course 1 (IK-1)
From Institute for Theoretical Physics II / University of Erlangen-Nuremberg
- 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
Contents
Preliminary program
Lecture notes
- Lectures 1-2 (PDF)
- Lecture 3 (PDF)
- Lectures 4-5 (PDF)
- Lectures 5-6 (PDF)
- Lecture 7 (PDF)
- Addendum to Lecture 7 (PDF)
- Lecture 8 (PDF)
- Lecture 9 (PDF)
- Lecture 10 (PDF)
- Lecture 11 (PDF)
- Lecture 12 (PDF)
- Lecture 13 (PDF)
- Lecture 14 (PDF)
- Addendum to Lecture 14 (PDF)
- Compendium on Angular Momentum (PDF)
- Lecture 15 (PDF)
- Lecture 16 (PDF)
- Lecture 17 (PDF)
- Lecture 18 (PDF)
- Lecture 19 (PDF)
- Lecture 20 (PDF)
- Lecture 21 (PDF)
- Examples for Lecture 21 (PDF)
- Addendum to Lecture 21 (PDF)
- Lecture 22 (PDF)
- Lecture 23 (PDF)
- Singular Value Decomposition (PDF)
Exercise sheets
- Worksheet 1 (PDF)
- Worksheet 2 (PDF)
- Addendum to Worksheet 2 (PDF)
- Worksheet 3a (PDF)
- Worksheet 3b (PDF)
- Worksheet 4 (PDF)
- Worksheet 5 (PDF)
- Worksheet 6 (PDF)
Quotations
- 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.
Bibliography
- 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
- The Feynman Lectures on Physics Online edition of "The Feynman Lectures on Physics"
- NIST Digital Library of Mathematical Functions Online library of mathematical functions
- Wolfram Online Integral Calculator Online integral calculator
- WolframAlpha Online mathematics, physics and more
- 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.
- Quantum Physics II Barton Zwiebach. 8.05 Quantum Physics II. Fall 2013. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.
- Quantum Physics III Aram Harrow. 8.06 Quantum Physics III. Spring 2016. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.
- C. Patrignani et al. (Particle Data Group), Chin. Phys. C 40, 100001 (2016). See table 44 "Clebsch-Gordan Coefficients, Spherical Harmonics, and d Functions" in the section "Mathematical Tools"
- Probability, Mathematical Statistics, Stochastic Processes A great website devoted to probability, mathematical statistics, and stochastic processes.
Relevant didactic articles
- Nine formulations of quantum mechanics, American Journal of Physics 70, 288 (2002) Quantum mechanics can be formulated in many different and equivalent ways. In this article the authors present a brief review (with annotated bibliography) of nine different formulations of quantum mechanics.
- 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 in quantum mechanics? American Journal of Physics 72, 348 (2004) A very interesting read about the actual meaning of a quantum state. Especially relevant is the second part of section II about possible instantaneous action-at-a-distance effects. Unfortunately the article suffer from numerous typos, please read also the "Erratum".
- 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."
- When is a quantum measurement? American Journal of Physics 54, 688 (1986) In this article Peres gives a clear analysis of a measurement in quantum mechanics and discuss the so-called "collapse" of the wavefunction.
- Is There a Quantum Measurement Problem? Phys. Rev. D 5, 1028 (1972) Another transparent analysis of the measurement problem in quantum mechanics. Note that the presentation of the subject given in this article is a bit advanced.
- Self‐adjointness and spontaneously broken symmetry, American Journal of Physics 45, 823 (1977) This article and the next two deal with the concept of self-adjoint extensions of operators. In this paper the author present a very clear and interesting physical model showing that, contrary to popular belief, the distinction between Hermitian, self-adjoint and essentially self-adjoint operators has physical roots.
- Self-adjoint extensions of operators and the teaching of quantum mechanics, American Journal of Physics 69, 322 (2001) A clear and concise exposition of the notion of self-adjoint extensions of operators, deficiency indexes and von Neumann theorem, at undergraduate level.
- Operator domains and self-adjoint operators, American Journal of Physics 72, 203 (2004) In the intention of the authors, the purpose of this paper is to supplement and expand the presentation given in the previous article. Many interesting examples are given.
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.