Turkish Journal of Physics
The quantization of reparametrized systems is discussed using the WKB approximation. The Hamilton-Jacobi function, the equations of motion and the wave function---which the conditions constrain in the semiclassical limit---are determined. The success of this approach is then demonstrated for two applications. The first is an illustrative example of nonrelativistic dynamics. The second is the well-known motion of a relativistic particle in an external electromagnetic field.
Singular Lagrangian, Parametrized systems, WKB Approximation.
NAWAFLEH, KHALED I.; RABEI, EQAB M.; and GHASSIB, HUMAM B. (2005) "Quantization of Reparametrized Systems Using the WKB Method," Turkish Journal of Physics: Vol. 29: No. 3, Article 3. Available at: https://journals.tubitak.gov.tr/physics/vol29/iss3/3