# A Two State System Spanned by Two Orthonormal Vectors

Consider a two state system spanned by two orthonormal vectors, |1> and |2>. The action of an operator Â is defined via:

Â|1> = 2|1> + i|2>

Â|2> = -i|1> + 3|2>

Find Â|ѱ> where

|ѱ> = |1> + |2>

Can you now verify your answer for Â|ѱ> by doing the calculation in matrix representation?

And then compute the four "matrix elements":

A_ij ≡ <i|Â|j>

Where i, j = 1, 2.

© BrainMass Inc. brainmass.com October 10, 2019, 7:41 am ad1c9bdddfhttps://brainmass.com/physics/quantum-physics/state-system-spanned-orthonormal-vectors-591533

#### Solution Summary

The solution shows, step by step, how to get the matrix representation of an operator under the given basis and show that the result is equivalent to direct calculation.

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