ge z-wave 45609 wiring question

I have a single light controlling one light. The box only has one black and one white. Can I use the ge z-wave 45609?

Thanks,

No.

The GE/Jasco 45609 requires a Line, Load and Neutral wire and you do not have these.

It sounds as though you have a switch loop, where the power comes in at the light and the switch is at the end of the circuit. The only devices that come to mind right now that can work in this scenario are the GE/Jasco 45612 Dimmer Switch and the Aeon Labs DSC26103-ZWUS In-Wall Micro Controller installed at the light.

Be aware that the 45612 is not suitable for LEDs or CFLs.