Related papers: Exponentially confining potential well
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…
Escape from a potential well is an extreme example of transient behavior. We consider the escape of the harmonically forced particle under viscous damping from the benchmark truncated weakly nonlinear potential well. Main attention is paid…
In this paper we prove sharp resolvent estimates for the magnetic Schr\"odinger operator in $\mathbb{R}^d$, $d\ge 3$, with $L^\infty$ short-range electric and magnetic potentials. We also show that these resolvent estimates still hold for…
We present a bi-confluent Heun potential for the Schr\"odinger equation involving inverse fractional powers and a repulsive centrifugal-barrier term the strength of which is fixed to a constant. This is an infinite potential well defined on…
We study low-energy expansion and high-energy expansion of reflection coefficients for one-dimensional Schr\"odinger equation, from which expansions of the Green function can be obtained. Making use of the equivalent Fokker-Planck equation,…
A new approximation scheme to the centrifugal term is proposed to obtain the $l\neq 0$ bound-state solutions of the Schr\"{o}dinger equation for an exponential-type potential in the framework of the hypergeometric method. The corresponding…
The exponential fitting technique uses information on the expected behaviour of the solution of a differential problem to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when…
We study the nonlinear Schr\"odinger equation with a periodic delta-function potential. This realizes a nonlinear Kr\"onig-Penney model, with physical applications in the context of trapped Bose-Einstein condensate alkaly gases and in the…
The optimized effective potential method is formulated as a convex minimization problem. This formulation does not require assumptions about $v$-representability nor functional differentiability. The formulation provides a natural framework…
We study the energy properties of a particle in one dimensional semi-harmonic rectangular wells and barriers. The integration of energies is obtained by solving a simple transcendental equation. Scattering states are shown to include cases…
We consider a real two-fluid system of compressible viscous fluids with a common velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an implicit function. The…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
The stationary one-dimensional tight-binding Schredinger equation with a weak diagonal long-range correlated disorder in the potential is studied. An algorithm for constructing the discrete binary on-site potential exhibiting a hybrid…
An alternative approximation scheme has been used in solving the Schroedinger equation for the exponential-cosine-screened Coulomb potential. The bound state energies for various eigenstates and the corresponding wave functions are obtained…
We study the homogenization of a stochastic Schr\"odinger equation with a large periodic potential in solid state physics. Denoting by $\varepsilon$ the period, the potential is scaled as $\varepsilon^{-2}$. Under a generic assumption on…
An expression for the Green function G(E;x_1,x_2) of the Schroedinger equation is obtained through the approximations of the path integral by n-fold multiple integrals. The approximations to Re{G(E;x,x)} on the real E-axis have peaks near…
Potential functionals have been introduced recently as an important tool for the analysis of coupled scalar systems (e.g. density evolution equations). In this contribution, we investigate interesting properties of this potential. Using the…
Spectral method related to Lame equation with finite-gap potential is used to study the optical cascading equations. These equations are known not to be integrable by inverse scattering method. Due to "partial integrability" two-gap…
In this paper we studied approximate solutions of the radial Schr\"odinger equation with the attractive Gaussian potential. We used asymptotic iteration method and variational method in order to obtain energy eigenvalues for any $n$ and $l$…
An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation which can be solved by iterative procedure to find the wave functions is…