Cathexis is a term to describe an investment of one's emotional energies, whether consciously or unconsciously, on a person
It comes from the greek word "kathexis", meaning "holding".
In psychoanalysis, emotional energy is expressed as libidinal energy. Sigmund Freud made the analogy between cathexis and electrical charge, saying that the former is a psychic equivalent to the latter.
Also, in the television series, Star Trek: Voyager, Cathexis was the title of an episode in which Chakotay goes brain-dead in an attack on his shuttle, and an alien presence inhabits members of the crew.