That's fair, thanks for the reply. Just commented because it looked similar to the Radarbox Airband antenna I picked up recently (https://www.amazon.com/AirNav-Airband-118-136-Outdoor-Connector/dp/B07XNKX18D) but you are absolutely correct.
About forty years ago I lived a mile from SJC. On quiet nights I could hear the physical ground operations equipment noise from my open bedroom window and on my radio scanner also.
What are you interested in listening to? Air to ground or ground operations at SJC?
How far are you from SJC? The ground ops are low powered xcvrs. You might not be able to hear them if you live more a few miles away. What is between you and SJC? Are there lots of large buildings between and SJC? How high up can you mount an antenna from the ground at your location?
The AG traffic can be heard at a much further distance. At some point in distance you will eventually only hear the Air side of the traffic.
Try out the antenna you just purchased. Try to mount the antenna as high as possible from the ground.
If it does not work well then there are low cost commercial vertical gain antennas at Amazon specifically for VHF aviation:
https://www.amazon.com/AirNav-Airband-118-136-Outdoor-Connector/dp/B07XNKX18D
Try to mount the antenna as high as possible from the ground.
The Silicon Valley is an extremely rich radio signal environment. For reception use a no gain discone antenna will capture tons of signals. For Amateur radio use either a high gain vertical or a rotatable multi element beam for more distant repeaters. Check out your local ham clubs.