relativistic massless harmonic oscillator we also provide a graphical presentation of numerical integration of equations of motion. Section III is devoted to the quantization of the massless relativistic harmonic oscillator. The Hamiltonian of the relativistic massless particle subject to the potential 1 $_{2}$κ $^{2}$x2 is given by where x and p are the position and the momentum of a particle, | p | = √ p 2 is the norm of the vector p (so c | p | is the kinetic energy of the particle), κ is a constant and c is the speed of light. Therefore, the Hamilton’s equations are We point out that an immediate consequence of Eq. (2.2) is ˙ x 2 = c $^{2}$, that is the length of velocity is c as should be for a massless particle. The familiar integrals of the motion in a central field [18] are the energy E and the angular momentum J : As a result of the conservation of the angular momentum J the motion is planar and we can restrict, without loss of generality, to the case of a particle moving in the ( x $^{1}$, x$^{2}$) plane. On passing to the polar coordinates x = ( x $^{1}$, x$^{2}$) = ( r cos ϕ, r sin ϕ ) and p = ( p $^{1}$, p$^{2}$) = ( p cos θ, p sin θ ), where r = | x | , and p = | p | , we obtain from Eq. (2.2) the following system: 3 ˙ r = c cos( θ − ϕ ) , ˙ ϕ = c r sin( θ − ϕ ) , ˙ p = − κ $^{2}$r cos( θ − ϕ ) , ˙ θ = κ $_{2}$r p sin( θ − ϕ ) . (2.5) E = c | p | + κ 2 2 x $^{2}$, (2.3) J = x × p . (2.4) ˙ x = c p | p | , ˙ p = − κ $^{2}$x . (2.2) H = c | p | + 1 2 κ $^{2}$x$^{2}$, (2.1) II. THE ANALYSIS OF THE CLASSICAL RELATIVISTIC MASSLESS HAR- MONIC OSCILLATOR