Foundations of Physics

, Volume 21, Issue 11, pp 1265–1284 | Cite as

A geometric approach to quantum mechanics

  • J. Anandan


It is argued that quantum mechanics is fundamentally a geometric theory. This is illustrated by means of the connection and symplectic structures associated with the projective Hilbert space, using which the geometric phase can be understood. A prescription is given for obtaining the geometric phase from the motion of a time dependent invariant along a closed curve in a parameter space, which may be finite dimensional even for nonadiabatic cyclic evolutions in an infinite dimensional Hilbert space. Using the natural metric on the projective space, we reformulate Schrödinger's equation for an isolated system. This metric is generalized to the space of all density matrices, and a physical meaning is proposed.


Hilbert Space Parameter Space Quantum Mechanic Physical Meaning Projective Space 
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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • J. Anandan
    • 1
    • 2
  1. 1.Department of Physics and AstronomyUniversity of South CarolinaColumbia
  2. 2.Max-Planck-Institute for Physics and AstrophysicsMunich 40Germany

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