Eigenfunction/Examples/SHM Equation
Jump to navigation
Jump to search
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