Work

Derivation of the Schrödinger Equation from Fundamental Principles

Year: 2026

Type: reference-entry

Abstract: Schrödinger’s path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrödinger equation for the particle’s wave function Ψ, assuming that the complex function Ψ(t,r→) has a meaning of the probability amplitude to find the particle at time t at point r→ and the relations E=ℏω, p→=ℏk→ expressing particle energy and momentum in terms of the frequency and wave vector of the associated probability wave.

Source: Encyclopedia

DOI: 10.3390/encyclopedia6020041

Authors: Wenzhuo Zhang, Anatoly Svidzinsky

Institution: Texas A&M University

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,207

Funders: National Science Foundation, U.S. Department of Energy, Welch Foundation, Air Force Office of Scientific Research