Don't really know how he could be anyone else.

Let me try to clear up some confusion here -- this man served in a Mississippi unit, not one from Arkansas. I only mentioned Arkansas because you said Burchfield lived there some years after the war ended. It's possible he applied for an Arkansas pension, but after checking the register, I don't see the name.

Here's a history of the Mississippi Cavalry Regiment mentioned earlier --
http://mississippiscv.org/MS_Units/2nd_MS_Partisan_Rangers_Cav.htm