Quantum Mechanics

  • Mikko Laine
  • Aleksi Vuorinen
Part of the Lecture Notes in Physics book series (LNP, volume 925)


After recalling some basic concepts of statistical physics and quantum mechanics, the partition function of a harmonic oscillator is defined and evaluated in the standard canonical formalism. An imaginary-time path integral representation is subsequently developed for the partition function, the path integral is evaluated in momentum space, and the earlier result is reproduced upon a careful treatment of the zero-mode contribution. Finally, the concept of 2-point functions (propagators) is introduced, and some of their key properties are derived in imaginary time.


Partition function Euclidean path integral Imaginary-time formalism Matsubara modes 2-point function 


  1. 1.
    R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Mikko Laine
    • 1
  • Aleksi Vuorinen
    • 2
  1. 1.AEC, Institute for Theoretical PhysicsUniversity of BernBernSwitzerland
  2. 2.Department of PhysicsUniversity of HelsinkiHelsinkiFinland

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