A Complete Course on Theoretical Physics pp 275-397 | Cite as

# Quantum Mechanics I

## Abstract

From the beginning of the book, but in particular in this chapter, we stress the inherent uncertainty (e.g., of an initial state). After discussing the usual formalism of the (im)proper Hilbert space with the Dirac bra and ket notation and the operator formalism, the Pauli principle is introduced at an early stage. A key topic is the uncertainty principle applied to the wave–particle duality, which is not without intricacies, and therefore rarely found elsewhere. Further topics are the Pauli and von Neumann equations, the Wigner function, the collision-free Boltzmann equation, parametric oscillators, (weak) coupling to the environment and the Markov approximation, the Liouville equation, absorption and emission, dissipation, and decoherence (a hot topic in modern science). There is a list of 45 problems.

## References

- 1.W. Heisenberg,
*The Physical Principles of the Quantum Theory*(Dover, 1930)Google Scholar - 2.J. von Neumann,
*Mathematische Grundlagen der Quantentheorie*(Springer, Berlin, 1968), p. 4Google Scholar - 3.P. Güttinger, Z. Phys.
**73**, 169 (1931)ADSCrossRefGoogle Scholar - 4.D.T. Pegg, S.M. Barnett, Europhys. Lett.
**6**(483) (1988). Phys. Rev. A**39**(1665) (1989)ADSCrossRefGoogle Scholar - 5.E.U. Condon, G.H. Shortley,
*The Theory of Atomic Spectra*(Cambridge University Press, 1935)Google Scholar - 6.O.L. deLange, R.E. Raab, Phys. Rev. A
**34**(1650) (1986)Google Scholar - 7.M. Abramowitz, I.A. Stegun,
*Handbook of Mathematical Functions*(Dover, New York, 1964)zbMATHGoogle Scholar - 8.E. Stiefel, A. Fässler,
*Group Theoretical Methods and Their Applications (Birkhäuser–Springer*(, Heidelberg, 1992)Google Scholar

## Suggestions for Textbooks and Further Reading

- 9.C. Cohen-Tannoudji, B. Diu, F. Laloè,
*Quantum Mechanics 1–2*(Wiley, New York, 1977)zbMATHGoogle Scholar - 10.R. Dick,
*Advanced Quantum Mechanics: Materials and Photons*(Springer, New York, 2012)CrossRefGoogle Scholar - 11.P.A.M. Dirac:
*The Principles of Quantum Mechanics*(Clarendon, Oxford)Google Scholar - 12.A.S. Green:
*Quantum Mechanics in Algebraic Representation*(Springer, Berlin)Google Scholar - 13.W. Greiner,
*Quantum Mechanics—An Introduction*(Springer, New York, 2001)zbMATHGoogle Scholar - 14.G. Ludwig,
*Foundations of Quantum Mechanics*(Springer, New York, 1985)zbMATHGoogle Scholar - 15.L.D. Landau, E.M. Lifshitz:
*Course of Theoretical Physics Vol. 3—Quantum Mechanics, Non-Relativistic Theory*3rd edn. (Pergamon, Oxford, London, 1977)Google Scholar - 16.A. Messiah:
*Quantum Mechanics I–II*(North-Holland, Amsterdam, 1961–1962)Google Scholar - 17.C. Itzykson, J. Zuber,
*Quantum Field Theory*(McGraw-Hill, New York, 1980)zbMATHGoogle Scholar - 18.D. Jackson,
*Mathematics for Quantum Mechanics*(Benjamin, New York, 1962)Google Scholar - 19.J.M. Jauch, F. Rohrlich,
*The Theory of Photons and Electrons. The Relativistic Quantum Field Theory of Charged Particles with Spin One-half*(Springer, Berlin, 1976)Google Scholar - 20.W. Nolting,
*Theoretical Physics 6—Quantum Mechanics—Basics*(Springer, Berlin, 2017)zbMATHGoogle Scholar - 21.W. Nolting,
*Theoretical Physics 7—Quantum Mechanics—Methods and Approximations*(Springer, Berlin, 2017)zbMATHGoogle Scholar - 22.P. Roman:
*Advanced Quantum Theory*(Addison-Wesley, Reading)Google Scholar - 23.J.J. Sakurai,
*Advanced Quantum Mechanics*(Addison-Wesley, Reading MA, 1967)Google Scholar - 24.J.J. Sakurai, J. Napolitano,
*Modern Quantum Mechanics*, 2nd edn. (Addison-Wesley, Boston, 2011)zbMATHGoogle Scholar - 25.F. Scheck,
*Quantum Physics*, 2nd edn. (Springer, Berlin, 2013)CrossRefGoogle Scholar - 26.F. Schwabl:
*Quantum Mechanics*(Springer, Berlin)Google Scholar