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}
}
  • C. Clark
  • Published 1 May 1996
  • Physics, Mathematics
  • Journal of Physics B
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. 

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References

SHOWING 1-10 OF 26 REFERENCES
Closed-form solutions of the Schrödinger equation for a model one-dimensional hydrogen atom
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
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.
  • Su, Eberly
  • Physics
    Physical 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.
TLDR
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
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?
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
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.
TLDR
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
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
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