Question

A real operator A satisfies the lowest order equation. A² − 4A + 3 = 0 

(a) Find the eigen values of A 

(b) Find the eigen states of A 

(c) Show that A is an observable.

Answer 1

(a) As A satisfies a quadratic equation it can be represented by a 2 × 2 matrix. Its eigen values are the roots of the quadratic equation

(c) As A = A^† , A is Hermitian and hence an observable.