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A basic principle of solutions of *linear* differential (often wave) equations, ensuring that the sum ("superposition") of two solutions is automatically a solution as well. Conversely, solutions (amounting to quantum states in quantum mechanics, since the Schrödinger equation is linear) can be represented as a sum of two or more other distinct solutions, and so can be Fourier/eigenstate resolved to enhance mathematical tractability.

Summing $$Y_1 = a_1 \, e^{i(\omega_1 t - k_1 x)} = a_1 \cos(\omega_1 t - k_1 x) + i \, a_2 \sin(\omega_1 t - k_1 x)$$ and $$Y_2 = a_2 \, e^{i(\omega_2 t - k_2 x)} = a_2 \cos(\omega_2 t - k_2 x) + i …
answered Apr 7 by Drubbels