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Feynman path integrals in quantum mechanics and statistics


  • Propagator and Green function
  • Path integral formulation of the propagator
  • Solution of some one-dimensional problems
    • Free particle
    • Free particle on a ring
    • Infinite potential well
    • Harmonic oscillator
  • Semiclassical approximation
    • Saddle point approximation
    • Saddle point approximation of the path integral
    • Van Vleck determinant
    • Change of stability of classical paths
    • Energy dependent Green function
    • Density of states for one-dimensional systems
    • Density of states in higher dimensions
  • Imaginary-time path integrals
    • Path-integral representation of the equilibrium density matrix
    • Harmonic oscillator in imaginary time
    • Tunnel spitting in a double-well potential
    • Decay of metastable states
      • Classical paths
      • Decay rate in the thermally activated regime
      • Decay rate at zero temperature
  • Dissipative quantum systems
    • Heat bath
    • Elimination of the heat bath within the path-integral formalism
    • Some results for dissipative quantum systems