# Eigen Value and Eigen Function

## Eigen Value and Eigen Function

If an operator Â operates on a well behaved function ƒ to give the same function but multiplied by a constant, then the constant is called*eigen value*of the operator and the function ƒ is called the

*eigen function*. The equation is called

*eigen value equation*.

A typical eigen value equation is-

ÂΨ = EΨ

Where, Â is an operator, E is the eigen value and Ψ is the wave function.

Example- if the function ƒ = e

^{−ax}is acted upon by the operator d/dx, the result is

d/dx(e

^{−ax}) = −a(e

^{−ax}).

Therefor, (−a) is the eigen value and e

^{−ax}is the eigen function of the operator d/dx.

## Show that the function Ψ = Sin2x is not the eigen function of operator d/dx but of d^{2}/dx^{2}?

Answer: Click Here
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