Explain Eigen values and Eigen function with suitable example.

Eigenvalues:-

The permissible values that a dynamical variable may have are those given by αφ = aφ, where φ is the eigenfunction of the operator α that corresponds to the observable whose permissible values are a.

This postulate can be stated in the form of an equation as

                    α operator φwave function = a constant . (eigenvalue)φ.wave function

If performing the operation on the wavefunction yields the original function multiplied by a constant, then φ is an eigenfunction of the operator α. This can be illustrated by letting φ = e2x and the operator α = d/dx. Then operating on the function with the operator gives dφ/dx =2e 2x =constant·e2x 

Therefore, e2x is an eigenfunction of the operator α with an eigenvalue 2.