In this problem examples of non normalizable and hence unphysical solutions of the Schr\"odinger equation of the harmonic oscillator are discussed.
(a) Is ex2/(2x02) an eigenfunction of the operator n^=a†a?
(b) Can you give a divergent eigenfunction of n^ with eigenvalue 0?
(c) Why don't these unphysical solutions occur in the algebraic method?