This scene crucially slows down the action, which heightens the tension of the viewer. It also serves to dramatize this sequence. Arbogast is also filmed in one long sequence, which slows down the scene. The long shot cements Arbogast as a victim in the viewer's eye.
By showing a close up shot of the door slowing opening as Arbogast walks up the stairs, the viewer is given advance warning of the impending sequence. This heightens tension by realizing the viewers thought of something happening to Arbogast.
This movie is part of the historical "Psychological Horror Cycle," characterized by the horror coming from something ordinary. This scene takes the audience on an emotional ride as Arbogast discovers what really happens at Bate's Motel. By introducing Arbogast as a competent detective, Hitchcock reassures the viewer; then unsettles the viewer by killing him.
In conclusion, this scene serves to show how Hitchcock is able to easily manipulate the viewer's emotions in his film. Psycho.