相关论文: New approximate radial wave functions for power-la…

Using exact solutions, we show that it is in principle possible to regard waves and particles as representations of the same underlying geometry, thereby resolving the problem of wave-particle duality.

We investigate radiative corrections to K --> 3 pi decays. In particular, we extend the non-relativistic framework developed recently to include real and virtual photons and show that, in a well-defined power counting scheme, the results…

An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The…

We report on progress concerning the partial wave analysis of higher correlation functions in conformal quantum field theory.

We derive analytically some general features of the power-law sensitivity curve. They include an exact parametric equation, a formula for the peak sensitivity and a proof of convexity in log-log plot. A few conceptual points are also…

First, a misconception about the spectrum of a confined particle is evidentiated. Then, the results are shown to be incorrect by means of a counter-example, an explicit preparation for the probe is given that yields an arbitrary…

A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of…

The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise…

I derive directional wave equations useful for pulses propagating in beam, rod, pipe, and disk geometries by using a cylindrical coordinate system; the scheme works equally well for either long multi-cycle or single-cycle ultrashort pulses.…

The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The result for real-valued systems are simplified and a pair of basis functions is found. These bases are a…

It is shown how the Canonical Function approach can be used to obtain accurate solutions for the distorted wave problem taking account of direct static and polarisation potentials and exact non-local exchange. Calculations are made for…

Rotating wave approximation (RWA) plays a key rule in quantum optics to solve some Schr\"{o}dinger equation approximately. For example, it is well known that RWA has been used to calculate the transition probability. However, so far no one…

We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…

In order to investigate corrections to the common KdV approximation for surface water waves in a canal, we derive modulation equations for the evolution of long wavelength initial data. We work in Lagrangian coordinates. The equations which…

Complex potentials are constructed as Darboux-deformations of short range, radial nonsingular potentials. They behave as optical devices which both refracts and absorbs light waves. The deformation preserves the initial spectrum of energies…

In this paper we apply a well-tested approximation of electron Coulomb distortion effects to the exclusive reaction (e,e'p) in the quasielastic region. We compare the approximate treatment of Coulomb distortion effects to the exact…

We present the wakefield conformal mapping technique that can be readily applied to the analysis of the radiation generated by an ultra-relativistic particle in the step transition and a collimator. We derive simple analytical expressions…

The effects of quadratic order terms in the dispersion matrix near a mode conversion are considered. It is shown that including the corrections due to these quadratic terms gives a better matching between the local solution in the mode…

A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the…

In this note I introduce a mysterious approximation called the rotating wave approximation (RWA) to undergraduates or non-experts who are interested in both Mathematics and Quantum Optics. In Quantum Optics it plays a very important role in…