Related papers: Uniform WKB approximation of Coulomb wave function…
In this paper we prove some uniform asymptotic estimates for confluent hypergeometric functions making use of the steepest-descent method. As an application, we obtain Strichartz estimates with loss of angular derivatives for the massless…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…
An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order $1/k^2$, where $k$ is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are…
Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed…
Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…
The Sommerfeld factor for arbitrary partial wave processes is derived in the non-relativistic limit. The s-wave and p-wave numerical results are presented for the case of Yukawa interactions. An approximate analytic expression is also found…
We discuss the problem of constraining cosmological parameters with cosmic microwave background band--power estimates. Because these latter are variances, they do not have gaussian distribution functions and, hence, the standard…
Radial wave functions for power-law potentials are approximated with the help of power-law substitution and explicit summation of the leading constituent WKB series. Our approach reproduces the correct behavior of the wave functions at the…
In this paper, the WKB method is extended to be applicable for conformable Hamiltonian systems where the concept of conformable operator with fractional order $\alpha$ is used. The WKB approximation for the $\alpha$-wavefunction is derived…
In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. It is illustrated through the particular cases of the harmonic oscillator and the Coulomb potential. In this kind of system the…
A new technique towards finding asymptotic normalization coefficients in the complex-ranged Gaussian basis is presented. It is shown that a diagonalisation procedure for the total Hamiltonian matrix in the given basis results in…
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…
We demonstrate that in semiconductor quantum dots wave functions probed by imaging techniques based on local tunneling spectroscopies like STM show characteristic signatures of electron-electron Coulomb correlation. We predict that such…
We propose a general method for constructing system-dependent basis functions for correlated quantum chemical calculations. Our construction combines features from several traditional approaches: plane waves, localized basis functions, and…
Complete and physically adequate analytical and semi-analytical solutions have been obtained using a practical dimensionless form of kinetic equation assuming azimuthal symmetry and Maxwellian distributions of target plasma species.…
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…
Wave/Schr\"{o}dinger equations with potentials naturally originates from both the quantum physics and the study of nonlinear equations. The distractive Coulomb potential is a quantum mechanical description of distractive Coulomb force…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
We discuss the semi-classical gravitational wave corrections to Gauss's law, and obtain an explicit solution for the electromagnetic potential. The Gravitational Wave perturbs the Coulomb potential with a function which propagates to the…