Fractional quantization of holonomic constrained systems using fractional WKB approximation

Abstract

In this work, the fractional canonical quantization for holonomic constrained systems is examined using the fractional WKB approximation. The fractional Hamilton-Jacobi function is obtained. The solutions of the equations of motion are derived from this function. It is shown that these solutions are in exact agreement with using the fractional Euler-Lagrange equations and fractional Hamilton’s equations. Also, this function enables us to construct the suitable wave function and then to quantize these systems using the fractional WKB approximation. One example is examined to illustrative the formalism. PACS: 11. 10. Ef, 45. 20. –j, 45.20. Jj, 45. 10. Hj, 04. 60. Ds, 04.20.Fy