Crime and Punishment and the Big Q

My big question applies very much to Crime and Punishment. Raskolnikov murders an old woman and her sister because he believes that she is a waste of space. At times, Raskolnikov's personality seems to change and he believes that he was wrong to murder the woman, but for the most part he believes that the murder was justified. Raskolnikov felt that the old pawnbroker was not helping anyone and really served no purpose, so he killed her. Because he had justification for the killing, Raskolnikov didn't feel like he had done anything wrong.