Modelos semiclásicos en la representación de estados coherentes

Abstract

We present a study of semiclassical approximations to quantum magnitudes in the Bargmann representation. Firstly, a description of the WKB model in the coordinate representation is given, including a quantitative validity condition for the approximation. Subsequently, we define the coherent states and their main properties, as well as the Bargmann states (non-normalized coherent states), which allows us to develop the semiclassical approximations in the new representation. Both stationary and time-dependent Schr¨odinger equations are solved, stablishing a comparison with the results for the wavefunction coming from the coordinate representation formalism. The energy spectrum is also studied. As we will prove, the intrinsic complex structure of Bargmann representation leads us to an extension to the complex plane, where the concept of analyticity plays a fundamental role. Finally, we illustrate some advantages of the formalism we have introduced through its application to a particular stationary system (the harmonic oscillator), achieving an integral expression for the Hermite polynomials.