# Fermion propagator in an external potential and generalized Airy functions

## TL;DR

This paper investigates the fermion propagator in a time-dependent external potential in 0+1 dimensions, expressing it through generalized Airy functions and analyzing their properties.

## Contribution

It introduces generalized Airy functions to describe the fermion propagator in specific time-dependent potentials, extending the standard Airy functions.

## Key findings

- Propagator expressed via generalized Airy functions for quadratic potentials.
- Generalized Airy functions reduce to standard Airy functions in certain limits.
- Properties of these functions are systematically studied.

## Abstract

We study the behavior of the fermion propagator in an external time dependent potential in 0+1 dimension. We show that, when the potential has upto quadratic terms in time, the propagator can be expressed in terms of generalized Airy functions (or standard Airy functions depending on the exact time dependence). We study various properties of these new generalized functions which reduce to the standard Airy functions in a particular limit.