Analytical method to solve a partial differential equation

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- Separation of variables Analytical method to solve a partial differential equation

Separation of variables

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:

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

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Applications of Lie groups to differential equations

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