Rules of Quantum Mechanics

  • Alessandro TetaEmail author
Part of the UNITEXT for Physics book series (UNITEXTPH)


We use the language developed in Chap.  4 to give a mathematically rigorous formulation of the rules of Quantum Mechanics. The aim is to provide the theoretical instruments to study elementary quantum mechanical problems. We also add some comments and explanations to clarify the meaning of the rules and we mention the foundational problem connected with the measurement process. We conclude describing the approach to a quantum mechanical problem from the point of view of Mathematical Physics.


  1. 1.
    von Neumann, J.: Mathematical Foundations of Quantum Mechanics. Princeton University Press, Princeton (1955)zbMATHGoogle Scholar
  2. 2.
    Dell’Antonio, G.: Lectures on the Mathematics of Quantum Mechanics. Atlantis Press (2015)CrossRefGoogle Scholar
  3. 3.
    Dimock, J.: Quantum Mechanics and Quantum Field Theory. Cambridge University Press, Cambridge (2011)CrossRefGoogle Scholar
  4. 4.
    Faddeev, L.D., Yakubovskii, O.A.: Lectures on Quantum Mechanics for Mathematics Students. AMS (2009)Google Scholar
  5. 5.
    Hall, B.C.: Quantum Theory for Mathematicians. Springer, New York (2013)CrossRefGoogle Scholar
  6. 6.
    Strocchi, F.: An Introduction to the Mathematical Structure of Quantum Mechanics, 2nd edn. World Scientific, Singapore (2008)Google Scholar
  7. 7.
    Thirring, W.: Quantum Mechanics of Atoms and Molecules. Springer, New York (1981)zbMATHGoogle Scholar
  8. 8.
    Reed, M., Simon, B.: Methods of Modern Mathematical Physics, I: Functional Analysis. Academic Press, New York (1980)zbMATHGoogle Scholar
  9. 9.
    Fasano, A., Marmi, S.: Analytical Mechanics. Oxford University Press, New York (2006)zbMATHGoogle Scholar
  10. 10.
    Feynman, R., Leighton, R.B., Sands, M.L.: The Feynman Lectures on Physics, vol. III. Addison Wesley Publ, Com (2005)zbMATHGoogle Scholar
  11. 11.
    Ghirardi, G.C.: Sneaking a Look at God’s Cards—Unraveling the Mysteries of Quantum Mechanics. Princeton University Press, Princeton (2007)zbMATHGoogle Scholar
  12. 12.
    Isham, C.J.: Lectures on Quantum Theory. Imperial College Press (1995)Google Scholar
  13. 13.
    Bell, J.: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press (1987)Google Scholar
  14. 14.
    Bricmont, J.: Making Sense of Quantum Mechanics. Springer (2016)CrossRefGoogle Scholar
  15. 15.
    Dürr, D., Teufel, S.: Bohmian Mechanics. The Physics and Mathematics of Quantum Theory. Springer, Berlin (2009)zbMATHGoogle Scholar
  16. 16.
    Bohr, N.: The quantum postulate and the recent development of atomic theory. Nature 121, 580–590 (1928)ADSCrossRefGoogle Scholar
  17. 17.
    Amrein, W.O.: Hilbert Space Methods in Quantum Mechanics. EPFL Press, Lausanne (2009)zbMATHGoogle Scholar

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica Guido CastelnuovoUniversità degli Studi di Roma “La Sapienza”RomeItaly

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