The Feynman Integrand for the Perturbed Harmonic Oscillator as a Hida Distribution
Mario Cunha, Custodia Drumond, Peter Leukert, Jose Luis Silva, Werner, Westerkamp
TL;DR
This paper demonstrates that the Feynman integrand for a harmonic oscillator with an external potential can be rigorously formulated as a Hida distribution within White Noise Analysis, providing a mathematical foundation for quantum path integrals.
Contribution
It introduces a rigorous construction of the Feynman integrand as a Hida distribution using White Noise Analysis, extending the mathematical understanding of quantum path integrals.
Findings
Feynman integrand for harmonic oscillator is a Hida distribution
White Noise Analysis provides a rigorous framework for path integrals
Extension to external potentials broadens applicability of the method
Abstract
We review some basic notions and results of White Noise Analysis that are used in the construction of the Feynman integrand as a generalized White Noise functional. We show that the Feynman integrand for the harmonic oscillator in an external potential is a Hida distribution.
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Taxonomy
TopicsAdvanced Thermodynamics and Statistical Mechanics