Closed-form solutions of the Schrödinger equation for a class of smoothed Coulomb potentials
@article{Clark1996ClosedformSO, title={Closed-form solutions of the Schr{\"o}dinger equation for a class of smoothed Coulomb potentials}, author={Charles W. Clark}, journal={Journal of Physics B}, year={1996}, volume={30}, pages={2517-2527} }
An infinite family of closed-form solutions is exhibited for the Schrodinger equation for the potential . Evidence is presented for an approximate dynamical symmetry for large values of the angular momentum l.
9 Citations
The generalized Coulomb interactions for relativistic scalar bosons
- Physics
- 2016
Approximate analytical solutions of Duffin–Kemmer–Petiau (DKP) equation are obtained for the truncated Coulomb, generalized Cornell, Richardson and Song–Lin potentials via the quasi-exact analytical…
The Soft-Core Coulomb Potential in the Semi-Relativistic Two-Body Basis
- Physics
- 2013
We consider the soft-core Coulomb potential within a semi-relativistic two-body framework which arises from the spinless Salpeter equation after some approximations valid for heavy interacting…
Dirac eigenvalues for a softcore Coulomb potential in d dimensions
- Physics
- 2012
A single fermion is bound by a softcore central Coulomb potential V(r) = -v/(r^q + b^q)^(1/q), v>0, b>0, q \ge 1, in d>1 spatial dimensions. Envelope theory is used to construct analytic lower bounds…
Soft-core Coulomb potentials and Heun’s differential equation
- Mathematics
- 2010
Schrodinger’s equation with the attractive potential V(r)=−Z/(rq+βq)1/q, Z>0, β>0, q≥1, is shown, for general values of the parameters Z and β, to be reducible to the confluent Heun equation in the…
Localization of Dirac-like excitations in graphene in the presence of smooth inhomogeneous magnetic fields.
- PhysicsJournal of physics. Condensed matter : an Institute of Physics journal
- 2012
It turns out that the bound state solutions of the two-dimensional hydrogen atom problem are related to the spectra of graphene excitations in the presence of the 1/r (inverse-radial) magnetic field.
Tunneling Time, Exit Time and Exit Momentum in Strong Field Tunnel Ionization
- Physics
- 2016
Tunnel ionization belongs to the fundamental processes of atomic physics. It is still an open question when does the electron tunnel ionize and how long is the duration of tunneling. In this work we…
Identification of tunneling and multiphoton ionization in intermediate Keldysh parameter regime.
- PhysicsOptics express
- 2019
It is theoretically demonstrated that the numerical observable ionization delay time is a more reliable indicator for characterizing the transition from TI to MPI under different laser parameters.
References
SHOWING 1-10 OF 26 REFERENCES
Closed-form solutions of the Schrödinger equation for a model one-dimensional hydrogen atom
- Physics
- 1992
The authors have found an infinite number of closed-form solutions to the Schrodinger equation for a well known model atom, by treating its short-range cut-off parameter as an eigenvalue.
Variable time-step integrator for intense field dynamics
- Physics
- 1990
A modification of the well-known Lanczos algorithm is described that adapts the method to explicitly time-dependent solutions of the Schrodinger equation. This technique possesses the desirable…
Model atom for multiphoton physics.
- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1991
We describe in detail some properties of a one-dimensional model atom that has been used for the study of multiphoton processes. We discuss static properties of the atom such as its energy…
New class of resonance in the e + H+ scattering in an excimer laser field.
- PhysicsPhysical review letters
- 1987
Numerical evidence is reported on the numerical evidence of a new class of low-energy e+H/sup +/ scattering resonances which dominate the field-modified elastic and the inelastic scattering cross sections in the presence of a strong excimer laser.
Perturbation Method for Atoms in Intense Light Beams
- Physics
- 1968
The problem of interaction of atoms with intense light is reformulated via a time-dependent unitary transformation. An effective electronic binding potential is obtained. The effective perturbation…
Stabilization of atoms in superintense laser fields: Is it real?
- PhysicsPhysical review letters
- 1991
We present an argument based on classical mechanics that stabilization of real atoms in superintense laser fields requires substantially higher frequencies than it is suggested by the analysis of…
Quantum defect theory
- Physics
- 1983
Quantum defect theory (QDT) is concerned with the properties of an electron in the field of a positive ion and, in particular, with expressing those properties in terms of analytical functions of the…
Numerical simulations of multiphoton ionization and above-threshold electron spectra.
- PhysicsPhysical review. A, General physics
- 1988
An intensity-dependent ponderomotive shift of the ionization threshold is demonstrated, a free-electron scaling of the number of ATI peaks with intensity and frequency of the field is found, and the numerical simulations with two simple Keldysh-type models are compared.
Population trapping in short-pulse multiphoton ionization
- Physics
- 1996
We have studied population trapping in a one-dimensional model atom interacting with a short-pulse high-intensity laser, using Floquet analysis and direct numerical integration of the time-dependent…