• Corpus ID: 11943422

A Feynman-Kac Formula for Unbounded Semigroups

  title={A Feynman-Kac Formula for Unbounded Semigroups},
  author={Barry Simon},
  journal={arXiv: Mathematical Physics},
  • B. Simon
  • Published 27 July 1999
  • Mathematics
  • arXiv: Mathematical Physics
We prove a Feynman-Kac formula for Schrodinger operators with potentials V(x) that obey (for all \epsilon > 0): V(x) \geq - \epsilon |x|^2 - C_\epsilon. Even though e^{-tH} is an unbounded operator, any \phi, \psi \in L^2 with compact support lie in D(e^{-tH}) and is given by a Feynman-Kac formula. 

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