Eigenfunction/Examples/SHM Equation

Examples of Eigenfunction

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 $m$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): eigenfunction
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): eigenfunction