From our recently developed representation of the path integral in terms of coherent states of the dynamical group SU(1,1), we obtain the semiclassical limit as a large-$N$ limit. Specifically, the parameter $k=\frac{1}{2}(l+\frac{N}{2})$ which labels the relevant SU(1,1) representations plays the role of ${\hslash }^{-1\mathrm{}}$. A phase-integral quantization rule is given and used to calculate the energy eigenvalues for various isotropic anharmonic oscillators. We obtain results comparable to the first-order JWKB calculations even at $N=1\mathrm{}$.

• Received 19 October 1982

DOI:https://doi.org/10.1103/PhysRevD.28.1939