What question did this study set out to answer?

The aim is to derive the Schrödinger equation using fundamental principles rather than intuition.

February 8, 2026Open Access

Derivation of the Schrödinger Equation from Fundamental Principles

Key Points

The aim is to derive the Schrödinger equation using fundamental principles rather than intuition.
Derived the wave function Ψ based on probability amplitude concepts.
Assumed relationships between energy, frequency, momentum, and wave vector.
Utilized classical principles to connect quantum mechanics with its foundational equations.
Derivation of the Schrödinger equation for a particle's wave function Ψ was achieved.
Established relationships E=ℏω and p→=ℏk→ to illustrate quantum mechanics principles.

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.

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