Eigen Value and Eigen Function

Eigen Value and Eigen Function

If an operator  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 d²/dx²?

Answer: Click Here

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