Rayleigh-Ritz Variational Method for Spin-Less Relativistic Particles

n relativistic quantum theory, for many problems of physical interest, exact solutions are not available even in one dimension. Therefore it is highly desirable to investigate and apply the methods of approximation which work in non-relativistic cases to relativistic conditions. In this article we extend the well-known Rayleigh-Ritz variational method used in non-relativistic quantum mechanics to relativistic case. To test the validity of the approach we apply the method to relativistic spin-less quantum particles under different potential conditions, such as free particle in an infinite well, charged particle in a coulomb potential and particle in an infinite range linear potential. The results are then compared with those of exact methods, comparison validates the method to a very good extent.