Il Nuovo Cimento A (1965-1970)

, Volume 109, Issue 11, pp 1567–1580 | Cite as

On the minimum set of physical assumptions leading to the Schrödinger equation

  • S. Bobbio
  • G. Marrucci


The way of obtaining the Schrödinger equation for a quantum particle in an electromagnetic field is revisited, showing that very few physical assumptions are required. In fact, after having introduced the general formalism of non-relativistic quantum mechanics, it is shown that the structure of the Schrödinger equation for a spinless particle is obtained merely by requiring continuity of space and time, and covariance with respect to Galilean transformations. Both the Correspondence and Uncertainty principles then become «theorems».

PACS 03.65.Bz

Foundations, theory of measurement, miscellaneous theories (including Aharonov-Bohm effect, Bell, inequalities, Berry's phase) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Dirac P. A. M.,The Principles of Quantum Mechanics, 2nd edition (Clarendon, Oxford) 1935.Google Scholar
  2. [2]
    Heisenberg W.,The Physical Principles of the Quantum Theory (University of Chicago) 1930.Google Scholar
  3. [3]
    Landau L. andLifschitz E.,Mécanique quantique (MIR, Moscow) 1967.Google Scholar
  4. [4]
    Bohm D.,Quantum Theory (Prentice Hall, Englewood Cliffs, N.J.) 1951.Google Scholar
  5. [5]
    von Neumann J.,Mathematical Foundations of Quantum Mechanics (Princeton University Press) 1955.Google Scholar
  6. [6]
    Messiah A.,Quantum Mechanics (North-Holland Publ., Amsterdam) 1961.Google Scholar
  7. [7]
    Blokhintsev D. J.,Quantum Mechanics (D. Reidel Publ., Dordrecht) 1963.Google Scholar
  8. [8]
    Feynman R.,The Feynman Lectures on Physics, Vol.3 (Addison Wesley Publ., Reading, Mass.) 1965.Google Scholar
  9. [9]
    Davydov A. S.,Meccanica Quantistica (MIR, Moscow) 1981.Google Scholar

Copyright information

© Società Italiana di Fisica 1996

Authors and Affiliations

  • S. Bobbio
    • 1
  • G. Marrucci
    • 1
  1. 1.School of EngineeringUniversity Federico IINapoliItaly

Personalised recommendations