Operators can also be expressed as matrices and wave functions as column vectors. The operator matrix

acts on the wave function (a, b) according to the rule

In words, the 2 × 2 matrix operator acting on the two-element column wave function generates another two-element column wave function. If the wave function generated by the operation is the original wave function multiplied by a constant, the wave function is an eigenfunction of the operator. What is the effect of the operator

on the column vectors (1, 0), (0,1), (1,1), and (ˆ’1,1)? Are these wave functions eigenfunctions of the operator? See the Math Supplement (Appendix A) for a discussion of matrices.    

Transcribed Image Text:

(а в в Въ ´a aa + Bb ба + Sa + eb