Introducing the effect of spin in the Hamilton-Jacobi equation: Application in the hydrogen atom

A new solution for the two-body problem is presented here. Its development is in accordance with fundamental principles of special relativity theory, i.e. the rest frame energy of any particle must be finite. Therefore, potentials are finite everywhere presenting no renormalization problems. As an example, this new approach is applied to the hydrogen atom problem, allowing introduction of 'spin' effects in the Hamilton-Jacobi equation through an equivalent ordinary orbital angular momentum, which behaves like the electron spin. The correct energy eigenvalues are obtained from the phase of the wave function through Sommerfeld-like path integrals.