Path Integrals in Quantum and Statistical Mechanics

Abstract

AbstractThe path integral formulation of quantum mechanics is an alternative to Schrödinger’s wave mechanics or Heisenberg’s matrix mechanics. The path integral method allows for a uniform treatment of quantum mechanics, statistical mechanics and quantum field theory and can be regarded as a basic tool in modern theoretical physics. We introduce and discuss the path integral for quantum mechanics and quantum statistics. Thereby the time-evolution kernel, correlation functions, generating functionals of correlation functions and thermodynamic potentials are given by sums, or functional integrals, over an infinity of possible trajectories. The results are applied to the free particle and the harmonic oscillator. Both the semi-classical and high-temperature expansions of the partition function are considered in the end-of-chapter problems.KeywordsPartition FunctionImaginary TimeCanonical Partition FunctionWightman FunctionPath Integral MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.