Is there any solid evidence showing that Hamlet was jealous of Claudius?
Some critics have suggested that Hamlet's anger at his mother for marrying Claudius is based on his own sexual desire for his mother; in other words, he is upset with his mother for marrying Claudius because, subconciously, he would have liked to marry her himself. (See second link below.)
Sigmund Freud interpreted Hamlet's reluctance to kill Claudius according to his famous Oedipal theory, that sons wish to kill their fathers and become intimate with their mothers. Freud explained that Hamlet is jealous of Claudius because Claudius has done what he (Hamlet) has always wished to do: kill the King and marry Gertrude. Hamlet is therefore reluctant to kill Claudius, because by doing so he would be killing his own hero, a man who is in a way an embodiment of himself. (See second link below.)
Like all theories, this one can be challenged. Some critics point out that Hamlet expresses great love and admiration for his father. These expressions do not seem to fit with Freud's explanation that Hamlet always wished to kill his father. (See first link below.)