Weak Form of Differential Equations and Differential Identities

TL;DR

This paper introduces a weak form framework for differential equations and identities, inspired by quantum mechanics, demonstrating that the Schrödinger equation can be viewed as a weak form of the Euler-Lagrange equation.

Contribution

It proposes a novel weak form approach for differential equations and identities, connecting quantum mechanics with classical variational principles.

Findings

Schrödinger equation is a weak form of Euler-Lagrange equation

Weak forms extend classical differential identities

Framework bridges quantum mechanics and variational calculus

Abstract

Inspired by quantum mechanics, we introduce a weak form of solutions for differential equations and differential identities like Stokes theorem and Euler-Lagrange equation. We show that Schr\"{o}dinger equation is a weak from of the classical Euler-Lagrange equation.