Which of the following function must NOT be a valid wavefunc

Which of the following function must NOT be a valid wavefuncitons? (multiple answer possible) These functions can be normalized if needed. No explanation is needed. (i) (x) = in(x) - infinity

Solution

1. graph ( ii) quantum mechanicaly is not valid since it does not show probability of finding a particle at far (ifinite) is not zero and hence it is opened graph from one side unlike graph (iii) which is closed.

2.(px -xp) sin x=(h/id/dx x - x h/i d/dx ) sinx

=h/i(d/dx x.sinx -x d/dx sinx)

=h/i(sinx+xcosx-xcox)=h/i sinx, hence sin x is eigen function of the given operator with eigen value h/i.