The following excerpt from Edgar Allan Poe's short story "The Tell-Tale Heart" explain why the narrator has "a light heart" when he opens the front door.

I then took up three planks from the flooring of the chamber, and deposited all between the scantlings. I then replaced the boards so cleverly, so cunningly, that no human eye—not even his—could have detected any thing wrong. There was nothing to wash out—no stain of any kind—no blood-spot whatever. I had been too wary for that. A tub had caught all—ha! ha!

When I had made an end of these labors, it was four o'clock—still dark as midnight. As the bell sounded the hour, there came a knocking at the street door. I went down to open it with a light heart,—for what had I now to fear?

The murderer has taken great pains to hide the body. He would have been successful in committing the perfect crime if he had not given himself away. In another short story, "The Imp of the Perverse," Poe identifies what he calls a natural human tendency to do exactly the wrong thing just out of perversity. The narrator of "The Tell-Tale Heart" allows his imagination to get away from him. He begins to think the policemen are playing mind games with him, because he can hear the heart beating so loudly and they act as if they hear nothing unusual. Finally the narrator breaks down and confesses. 

Poe probably included the statement, "I went down to open it with a light heart," because he wanted to stress that the narrator was not in the least conscious of his heart beating--but evidently what he was hearing during his interview with the policemen could only have been his own heart. He was much more anxious than he admitted to himself. Our bodies often give us away when we are trying out best to appear calm and poised. There were no such things as lie detectors in Poe's day, but a modern lie detector would have easily exposed the guilt of the nervous narrator of "The Tell-Tale Heart."