Eigenfunction/Examples
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Examples of Eigenfunctions
SHM Equation
Consider the differential equation describing simple harmonic motion (SHM):
- $\dfrac {\d^2 y} {\d x^2} + \lambda y = 0$
subject to the boundary conditions:
- $\map y 0 = 0$
- $\map y \pi = 0$
This has an eigenvalue $m^2$ with eigenfunction $\sin m x$ for all non-zero integer $m$.