Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Situational Awareness
ATC Issue All Types; Conflict NMAC
Air Traffic Control Issued Advisory / Alert; Flight Crew FLC complied w / Automation / Advisory
Human Factors
On the RNAV Visual 31 L between fixes WEMIR and CEKMA; SOCAL Approach witnessed a target (aircraft he was not talking to) pop up that was a threat to us.  He instructed us to stop descent immediately; the First Officer did a great job of arresting the descent; then Approach told us to immediately climb as TCAS instructed us to descend.  We followed TCAS and saw the single-engine turboprop pass over us by about 400 feet and in front of us by about one-half mile.  The FO re-established us on the approach and we landed without incident.The beautiful weather in Palm Springs and general aviation aircraft not talking to ATC was THE factor in this TCAS RA. ALWAYS follow TCAS.
Air carrier Captain reported TCAS RA Alert on approach to PSP airport.