Uniform Approximation for the Coherent-State Propagator Using a Conjugate Application of the Bargmann Representation

We propose a conjugate application of the Bargmann representation of quantum mechanics. Applying the Maslov method to the semiclassical connection formula between the two representations, we derive a uniform semiclassical approximation for the coherent-state propagator which is finite at phase space caustics.

Figure 1

Square modulus of diagonal propagator for fixed $z$. The lines correspond to the exact result (full line), bare semiclassical (dotted line), and uniform (dashed line).