Resummed Wentzel-Kramers-Brillouin Series: Quantization and Physical Interpretation

The Wentzel - Kramers - Brillouin approximation method applied to the Wigner function

An adaptation of the WKB method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between the phase $σ(\vec{r})$ of a wave function $\exp \left(\frac{i}{\hbar} σ(\vec{r}) \right)$ and its respective Wigner function is derived. Formulas to calculate the Wigner function of a product and of a superposition of wave functions are proposed. Properties of a Wigner function of interfering states are also investigated. Examples of this quasi - classical a…

薛定谔方程的交替Wentzel-Kramers-Brillouin近似：重新发现Bremmer级数及其推广

Alternating Wentzel-Kramers-Brillouin Approximation to the Schrödinger Equation: Rediscover the Bremmers series and beyond

提出一种交替WKB近似方法，通过ansatz和辅助条件得到耦合方程，经交替微扰解耦为Bremmer级数，并推导出通用量子化公式，在特定条件下简化为闭式量子化条件。

Tunnel Splitting in Asymmetric Double Well Potentials: An Improved WKB Calculation

We present an improved Wentzel-Kramers-Brillouin (WKB) calculation of tunnel splitting in one dimensional asymmetric double well potentials. We show that the tunnel splitting in general can have linear dependence on the bias energy, beside the well-known quadratic dependence. We demonstrate that the linear correction is greater than previously thought.

A semiclassical treatment of the interaction of non-uniform electric fields with the electric quadrupole moment of a neutral particle

By applying the WKB (Wentzel, Kramers, Brillouin) approximation, we analyse the interaction of the electric quadrupole moment of a neutral particle with radial electric fields produced by a non-uniform electric charge densities. Then, we show particular cases of this interaction where a discrete spectrum of energy can be achieved for the s-waves of the neutral particle.