Takahisa Okino Department of Applied Mathematics, Faculty of Science & Engineering, Oita University, Oita City, Japan okino@oita-u.ac.jp International Journal of Fundamental Physical Sciences (IJFPS) 9 3 48-54 September, 2019 2231-8186 https://doi.org/10.14331/ijfps.2019.330131 This paper theoretically derives the Schrödinger equation from diffusion theory, bridging Newtonian and quantum mechanics. By analyzing the elementary process of diffusion, the author establishes a universal expression of diffusivity linked to angular momentum, demonstrating that matter waves are intrinsic to all moving microparticles. The study confirms the De Broglie hypothesis and introduces an alternative matter-wave relation incorporating temperature. These findings reframe diffusion theory as foundational to quantum mechanics and suggest implications for nanotechnology in materials science. De Broglie hypothesis, Schrödinger equation, Markov process, Diffusion equation https://creativecommons.org/licenses/by-nc/4.0/