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Related Experiment Video

Updated: May 14, 2026

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

Lande subtraction method with finite integration limits and application to strong-field problems.

Tsin-Fu Jiang¹, Shih-Da Jheng, Yun-Min Lee

¹Institute of Physics, National Chiao-Tung University, Hsinchu 30010, Taiwan. tfjiang@faculty.nctu.edu.tw

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 2, 2013

Summary

Researchers developed a new Lande subtraction method using a finite momentum range (p∈(0,p_{max})) for improved accuracy in Coulomb problems. This practical approach enhances calculations for atomic physics, including strong-field ionization and harmonic generation.

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Area of Science:

Atomic and Molecular Physics
Quantum Mechanics
Computational Physics

Background:

The standard Lande subtraction method for Coulomb problems assumes an infinite momentum range (p∈(0,∞)).
Previous applications required extensive momentum ranges for sufficient accuracy, limiting practical calculations.
Accurate theoretical treatment of strong-field atomic phenomena is crucial.

Purpose of the Study:

To derive a supplementary Lande subtraction formulation with a finite momentum range (p∈(0,p_{max})).
To improve the accuracy and practicality of calculations for Coulomb problems.
To apply the new method to strong-field atomic ionization and high-order harmonic generation.

Main Methods:

Derivation of a supplementary Lande subtraction formulation with a restricted momentum coordinate (p∈(0,p_{max})).
Application of the finite momentum range formulation to calculate the hydrogenic eigenspectrum.
Implementation of the method for simulating strong-field atomic above-threshold ionization and high-order harmonic generation.

Main Results:

The supplementary formulation achieves dramatically improved accuracy for the hydrogenic eigenspectrum compared to the ordinary Lande formula using identical momentum grids.
The method demonstrates practical applicability with reasonably small values of p_{max}.
Successful application to complex phenomena like strong-field atomic above-threshold ionization and high-order harmonic generation.

Conclusions:

The proposed finite momentum space method offers a practical and accurate alternative for Coulomb problems.
This formulation significantly enhances the precision of atomic physics calculations.
The method provides a valuable new theoretical tool for studying strong-field atomic phenomena.