Three useful bounds in quantum mechanics - easily obtained by Wiener integration

TL;DR

This paper demonstrates how the Feynman-Kac formula can be used to derive three important inequalities in non-relativistic quantum mechanics in a clear and explicit manner.

Contribution

It provides a straightforward method to obtain key quantum mechanical bounds using Wiener integration techniques.

Findings

Derived three quantum inequalities using Feynman-Kac formula

Presented a self-contained, explicit derivation of bounds

Showed efficiency of Wiener integration in quantum bounds

Abstract

In a reasonably self-contained and explicit presentation we illustrate the efficiency of the Feynman-Kac formula for the rigorous derivation of three inequalities of interest in non-relativistic quantum mechanics.