After being convict of murder, Peterson joined over six hundred other men on death row nearly two months ago.
Spokesman Eric Messick says Peterson has adapted to an isolated existence at San Quentin.
"He has not been a management problem at all for staff. Staff says he's been very cooperative and seems to be adjusting quite normally."
Messick confirmed reports that Peterson has received marriage proposals.
"The subject was implied a few times on some early phone calls the first couple of days since we received him here at San Quentin. We still get an occasional phone call asking for mailing information or if he can receive pictures."
Messick says Peterson is allowed visitors a few times a week, but he can only talk to them through a transparent partition.
No execution date has yet been set.