Student explore the properties of an orthonormal basis using the Cartesian and \(S_z\) bases as examples.
The state vectors \(\left|{+}\right\rangle \) and \(\left|{-}\right\rangle \) form an orthormal basis. Orthonormal bases have properties listed below.
For each property, write an equation that illustrates the property for both:
The elements are norm 1.
The elements are orthogonal.