= Separation of variables
{wiki}
Technique to solve <partial differential equations>
Naturally leads to the <Fourier series>, see: <solving partial differential equations with the Fourier series>, and to other analogous expansions:
One notable application is the solution of the <Schrödinger equation> via the <time-independent Schrödinger equation>.
Bibliography:
* https://math.libretexts.org/Bookshelves/Differential_Equations/Book%3A_Differential_Equations_for_Engineers_(Lebl)/4%3A_Fourier_series_and_PDEs/4.06%3A_PDEs_separation_of_variables_and_the_heat_equation on <LibreTexts> for the <heat equation>