yes! (actually I wrote it wrong.. ans is C if BC is not applied) But this is a Gate question and the Ans key is staying ans should be A.... We can only get to that ans if we apply ...
but, exp i(k.r-wt) is also a free. particle wave function.. then why we are discarding it? and we are not told here to Apply any B.C.. then why we are applying this B. C?