  We derive an equivalent traveling wave form description for Dirac field. In
the non-relativistic limit, such form can reduce to inverse-Galilean
transformed Schrodinger-type equation. We find that, the resulting
two-component Schrodinger-type equation from the reduction of traveling wave
form description of Dirac field is different to the naive Galilean transformed
Schrodinger equation. Taking into account the interactions of the system to
electromagnetic field by adding proper forms of covariant derivative, the
traveling wave form description for Pauli equation can be similarly obtained in
the non-relativistic limit. Such descriptions allow one to choose arbitrary
convenient reference frame for quantum system involving spins. Using
Bargmann-Wigner formalism for field with arbitrary spin $s\geq 1/2$, which
satisfy Dirac-type equations in all its indices, the traveling wave description
for such a field can be similarly obtained from the traveling wave form
description of Dirac field, for example, for the spin-3/2 Rarita-Schwinger
field and spin-2 gravitational field.
