# A Feynman-Kac Formula for Unbounded Semigroups

@article{Simon1999AFF, title={A Feynman-Kac Formula for Unbounded Semigroups}, author={Barry Simon}, journal={arXiv: Mathematical Physics}, year={1999} }

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.

## 11 Citations

### Continuous integral kernels for unbounded Schrödinger semigroups and their spectral projections

- Mathematics
- 2004

### The Weyl Symbol of Schrödinger Semigroups

- Mathematics
- 2015

In this paper, we study the Weyl symbol of the Schrödinger semigroup e−tH, H = −Δ + V, t > 0, on $${L^2(\mathbb{R}^n)}$$L2(Rn) , with nonnegative potentials V in $${L^1_{\rm loc}}$$Lloc1 . Some…

### Trace Formulae and High Energy Asymptotics for the Stark Operator

- Mathematics
- 2003

Abstract In , we consider the unperturbed Stark operator H0 (i.e., the Schrödinger operator with a linear potential) and its perturbation H = H 0 + Vby an infinitely smooth compactly supported…

### Strong short-time asymptotics and convolution approximation of the heat kernel

- MathematicsAnnals of Global Analysis and Geometry
- 2018

We give a short proof of a strong version of the short-time asymptotic expansion of heat kernels associated with Laplace-type operators acting on sections of vector bundles over compact Riemannian…

### Schrödinger operators in the twentieth century

- Physics
- 2000

This paper reviews the past fifty years of work on spectral theory and related issues in nonrelativistic quantum mechanics.

### RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITÄT BONN

- 2007

lron toxicity is a widespread nutritional disorder of rice in wetlands characterized by large concentrations of reduced iron (Fe) in the soil solution. It is associated with poor water control,…

### An extensive exploration of three key quantitative approaches for pricing various financial derivatives

- Economics
- 2011

Options and other financial derivatives have become increasingly important in financial markets ever since Black and Scholes (1973) proposed an analytical and quantitative formula for valuing…

### A P ] 1 6 D ec 2 01 3 The Weyl symbol of Schrödinger semigroups

- 2013

## References

SHOWING 1-10 OF 14 REFERENCES

### Mathematical theory of Feynman path integrals

- Physics
- 1976

Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including…

### From Brownian Motion To Schrödinger's Equation

- Mathematics
- 1995

1. Preparatory Material.- 2. Killed Brownian Motion.- 3. Schrodinger Operator.- 4. Stopped Feynman-Kac Functional.- 5. Conditional Brownian Motion and Conditional Gauge.- 6. Green Functions.- 7.…

### Spectral and scattering theory of Schrödinger operators related to the stark effect

- Mathematics, Physics
- 1977

We analyze the spectral properties and discuss the scattering theory of operators of the formH=H0+V,H0=−Δ+E·x. Among our results are the existence of wave operators, Ω±(H, H0), the nonexistence of…

### Functional integration and quantum physics

- Physics
- 1979

Introduction The basic processes Bound state problems Inequalities Magnetic fields and stochastic integrals Asymptotics Other topics References Index Bibliographic supplement Bibliography.

### on,M ethods of M odern M athem aticalPhysics, I. FunctionalAnalysis (rev.ed.),A cadem ic Press,London,1980

- 1980

### Schr odinger sem igroups,B ull.A m er

- M ath.Soc
- 1982

### ethods of M odern M athem atical Physics, II. Fourier Analysis, Self-Adjointness,A cadem ic Press,London,1975

- 1975

### From B row nian M otion to Schr odinger's E quation

- 1995

### Fourier A nal ysis, Sel f-A djointness,A cadem ic P ress

- 1975

### FunctionalIntegration and Q uantum P hysics,A cadem ic P ress

- 1979