Main Question or Discussion Point
What is eigen value, eigen vector etc and what is their physical significance?
I disagree. In any case when an operator describes something physical, its eigenvectors have direct physical significance. They usually form a basis of the space involved, and the corresponding eigenvalues describe the effect of the operator on the basis vectors. So we have, in a way, "principal" directions of the operator.These need have no physical significance at all - the terminology is mathematical and describes a mathematical relationship.