Is exp (- mod(x)/a) an eigenfunction of momentum?

[sachi]

Is exp (- mod(x)/a) an eigenfunction of momentum. I know that this is not differentiable at x = 0, but does this completely disqualify it from being a momentum eigenfunction?

 

[Physics Monkey]

That state doesn't have the same derivative above and below zero, so clearly it isn't a momentum eigenstate.