Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Calculating multidimensional discrete variable representations from cubature formulas.

Ilan Degani1, David J Tannor

  • 1Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel. ilan.degani@weizmann.ac.il

The Journal of Physical Chemistry. A
|April 21, 2006
PubMed
Summary

This study provides a general solution for constructing multidimensional discrete variable representations (DVRs) using cubature formulas. This advances computational quantum mechanics by enabling efficient calculations of Hamiltonian operators.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Generalized kicked rotor: Periodic forcing with finite-width pulses and the role of shifting the kick.

Physical review. E·2026
Same author

The robustness of composite pulses elucidated by classical mechanics: stability around the globe.

Physical chemistry chemical physics : PCCP·2025
Same author

The geometry of the classical action in phase space.

The Journal of chemical physics·2025
Same author

Exploring the role of chaos in model recollision processes.

The Journal of chemical physics·2025
Same author

Control of concerted back-to-back double ionization dynamics in helium.

The Journal of chemical physics·2021
Same author

Communication: Systematic elimination of Stokes divergences emanating from complex phase space caustics.

The Journal of chemical physics·2018

Area of Science:

  • Computational Quantum Mechanics
  • Numerical Analysis
  • Theoretical Chemistry

Background:

  • Calculating multidimensional nondirect product discrete variable representations (DVRs) for Hamiltonian operators is a persistent challenge in computational quantum mechanics.
  • The concept of a "DVR set" was previously introduced as a general framework to address this problem.
  • Existing methods face limitations in constructing general multidimensional DVRs.

Purpose of the Study:

  • To present a general solution for calculating multidimensional DVR sets based on known cubature formulas.
  • To illustrate the method by computing new nondirect product cubature DVRs in 2D and on a sphere.
  • To explore finite basis representations (FBRs) derived from general cubatures and connect them to existing theories.

Main Methods:

Related Experiment Videos

  • Developed a general method for constructing multidimensional DVR sets from cubature formulas.
  • Calculated new nondirect product cubature DVRs on the plane and sphere using up to 110 points.
  • Investigated finite basis representations (FBRs) linked to general cubatures.

Main Results:

  • Successfully generated general solutions for multidimensional DVR sets tied to cubature formulas.
  • Computed several novel nondirect product cubature DVRs for planar and spherical geometries.
  • Established connections between the constructed DVR sets and novel perspectives on cubature involving commuting extensions of coordinate matrices.

Conclusions:

  • The presented construction provides a general method for calculating multidimensional DVR sets, resolving a previously unresolved problem.
  • This work offers a practical approach to generating DVRs for complex systems in computational quantum mechanics.
  • The findings bridge the gap between DVR theory and cubature methods, offering new interpretations of function spaces in numerical computations.