 Quantum-mechanical propagator in a constant force

ID: quantum-mechanical-propagator-in-a-constant-force

In units

ℏ = 1

, a particle of mass

m

with potential

V (q) = - Fq

q_{c} (t) = q_{0} + [(q_{1} - q_{0}) / T - FT / (2 m)] t + F t^{2} / (2 m)

S_{c} = \frac{m ( q _{1} - q _{0} ) ^{2}}{2 T} + \frac{FT ( q _{1} + q _{0} )}{2} - \frac{F ^{2} T ^{3}}{24 m}, K_{F} = \frac{m}{2 πi T} e^{i S_{c}} .

The fluctuation operator is the free one because the potential is linear. This is a special case of classical-path factorization of a quadratic path integral.

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