Laptop doesn't recognize 1Tb portable hard drive

This may be a power problem.

The WD My Passport is sold as a USB3 portable drive. Its Specs say, "USB 3.0 / USB 2.0 compatible". What this means is that it is designed for use as a USB3 device with a USB3 connection, BUT it will operate (within limits) on a USB2 connection. What limits? Both power and speed.

A USB3 port can supply to a connected device up to 0.9 amps, whereas USB2 was up to only 0.5 amps. There were VERY few USB2 "portable" HDD units able to work with that smaller current limit. What WAS done for USB2 units was that they came with a special cable that had TWO USB connectors on one end, and you had to plug both of them in to get enough power for it to run. The new USB3 port standard solved this problem, so these new units do not include such an odd cable. HOWEVER, the USB3 Portable HDD's still DO require more than 0.5 amps to operate. So when you plug one into an older-type USB2 port, they almost look like they are working, but don't really. Even in the few cases where they appear to work, it's risky because you may manage to write data to the drive, but the writing operation may cause lots of errors on the drive unit.

So, IF your experience is that this drive works on your desktop unit, but not on your laptop, there's a GOOD possibility that the desktop machine has a real USB3 port to use, and your laptop has only USB2. I assume you are using for both cases the USB3 cable that came with the unit. Even if your desktop has only USB2 ports, it is possible they are designed to supply more than the spec of 0.5 amps max to an attached device.

If power is your problem, I know of two solutions.
1. Get one of those old odd 2-headed USB2 Portable HDD special cables and use it with two USB2 ports from the laptop. That may get you working.
2. This I know works because I've done it with exactly this type of problem. But a POWERED USB3 Hub. That is, a Hub for the USB3 system that comes with its own "wall wart" or "power brick" that can supply all the power the ports on the Hub need. That is, the power supply unit should be able to supply at least 0.9 amps per port at 5 VDC, or a total of 4.5 Watts per port. (The tricky thing is some of them supply to the Hub at 12 VDC even though the ports output 5 VDC, and thus the important capacity number is the WATTS available from the power unit.) So a 4-port Hub needs at least 18W to 20W capacity. Then you use your drive's USB3 cable to connect it to the Hub, ensure the Hub has its power supply module plugged in, and connect the Hub to any USB2 OR USB3 port using any USB cable. This way the drive can get all the power it needs from the Hub, and can communicate with the host computer on either type of USB port.

Now, the other part of the "limits" I mentioned is data transfer speed. You can only achieve the faster data transfer rates of the new USB3 system if all of the components are of the USB3 design. By "all", I mean the drive (your is, of course), the connection cable(s) from the drive to the computer port, and the computer port itself. If either the computer port or the connecting cable is only USB2, then the performance speed will be at the older USB2 slower rate. But as long as you can solve the power supply issue as above, it will work.

You're welcome.