Statistical and Quantum Mechanics
Wick rotation connects statistical mechanics to quantum mechanics by replacing inverse temperature with imaginary time . Consider a large collection of harmonic oscillators at temperature . The relative probability of finding any given oscillator with energy is, where is Boltzmann's constant. The average value of an observable is, up to a normalizing constant,
Now consider a single quantum harmonic oscillator in a superposition of basis states, evolving for a time under a Hamiltonian . The relative phase change of the basis state with energy is where is Planck's constant. The probability amplitude that a uniform superposition of states evolves to an arbitrary superposition is, up to a normalizing constant,
Read more about this topic: Wick Rotation
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