The Ghostbusters film is somewhat unusual in that it spawned two separate novelisations. The Mueller version gives us a little more background about Egon and Ray's work at the university.
- Egon is (or rather was) a teaching Professor of Physics until he managed to get a grant to study parapsychology.
Spengler shook his head. They were worse than graduate students. “No.
No water. There’s nothing you can do.”
After some time at the university, Egon, Ray and Venkman created a department for the phsyical study of Parapsychology, largely as a backwater for their pet projects; Egon and Ray to study ghosts and Venkman so he can take advantage of impressionable 18 year olds. They're each Professors in this dept.
The senior Dr. Stantz plied Peter with alcohol while encouraging him
to talk about their work in parapsychology, a subject that brother
Carl held in equal repute with Communism and homosexuality.
- Egon's scientific experiments are varied and highly esoteric.
He had been the first scientist to hypnotize a hamster by subjecting
to it low-frequency radio waves. Peter tried it later and found that
it also worked on coeds. Egon, in an attempt to build a death ray, had
come up with a sonic gun that had little effect on people but set off
soft-drink cans at a hundred yards. After the night that Peter had
gotten drunk and taken it down to the local Coca-Cola warehouse, Egon
had insisted on dismantling it.
Interestingly, all three of the Ghostbusters seem to have dual PhD's; Egon in Physics and Parapsychology, Venkman in Psychology and Parapsychology and Ray in Engineering and Parapsychology although it's possible that all three managed to secure their second PHD while at the university.