Perhaps numerically will do.

There isn't any such notion as a ``rise''. A triangular potential is described by a Dirichlet boundary conditon, for instance at x=0 and by a linear boundary; so V(x) =0, for 0≤x≤a and V(x) = Ax+B for x>a; it's triangular when a=0. The solution of the Schrödinger equation can be found in terms of so-called Airy functions, or numerically. This is a standard exercise in quantum mechanics, nothing conceptually challenging. The spectrum is discrete.