It is also called wave mechanics because quantum mechanics governed by Schrodinger's wave equation in it's wave-formulation.

equation is a double differential relate to the energy of particle with wave function

For general waves...probably d'Alembert, who solved the one-dimensional wave equation. In quantum it would have to be Schrodinger.

Jean le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, Joseph-Louis Lagrange, and the quantum wave function: Erwin Schrödinger.

Erwin Schrodinger