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Quantum Mechanics

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

Abstract

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.

Keywords

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

Reference

  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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