Time Fractional Schro\"odinger Equation

TL;DR

This paper introduces a time fractional version of the Schrödinger equation that preserves core quantum properties and is equivalent to a fractional Hamiltonian PDE, expanding the mathematical framework of quantum mechanics.

Contribution

It presents a novel time fractional Schrödinger equation maintaining key quantum features, linking it to a fractional Hamiltonian PDE for the first time.

Findings

Maintains main quantum properties in the fractional extension

Establishes equivalence with a fractional Hamiltonian PDE

Expands the mathematical framework of quantum mechanics

Abstract

We propose a time fractional extension of the Schr{\"o}dinger equation that keeps the main mechanical and quantum properties of the classical Schr{\"o}dinger equation. This extension is shown to be equivalent to another well identified time first order PDE with fractional hamiltonian.