Can we incorporate the wave into the mass equation? Let's start with two equations. The first for kinetic energy and the second for the wavelength itself.

Here KE is kinetic energy, m is the mass and v its velocity.

KE = (1/2)mv^2

For the wave equation we have:

f = h/p

Where f is the frequency, h is Planck's constant and p is momentum. To incorporate kinetic energy into the equation the following steps are required.

KE = (1/2) mv^2

2KE = mv^2

2KEm = m^2v^2

2KEm = (mv)^2

Since momentum equals mv we can derive momentum to include kinetic energy using SQRT(2KEm). Then for the wavelength we have:

f = h/SQRT(2KEm)

We can never have zero kinetic energy because we always have zero point energy. Therefore KE has to be intrinsic to mass which means mass always has momentum. Only for purposes of mathematical derivation can we use rest mass. Since mv would require velocity to be a numerator we would be multiplying velocity with hbar so no we cannot incorporate the wave equation into a mass equation. The same can be said for the energy equation. This indicates that the wave is merely an effect of the motion of the particle through space. Either in a straight line path or via angular momentum. From this we can reach the conclusion that because the wave is not intrinsic it can be directly affected by the gravitational field. Since the gravitational field will affect trajectory.