More about the S=1 relativistic oscillator

Abstract

Following to the lines drawn in my previous paper about the S=0 relativistic oscillator I build up an oscillatorlike system which can be named as the S=1 Proca oscillator. The Proca field function is obtained in the framework of the Bargmann-Wigner prescription and the interaction is introduced similarly to the S=1/2 Dirac oscillator case regarded by Moshinsky and Szczepaniak. We obtained the intriguing rule of quantization: E = \hbar ω/2 for the parity states (-1)^j and E = \pm \hbar ω(j+1/2) for the parity states -(-1)^j. There are no radial excitations. Finally, I apply the above-mentioned procedure to the case of the two-body relativistic oscillator.