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Related Experiment Video

Updated: May 19, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Variational properties of the discrete variable representation: discrete variable representation via effective

Viktor Szalay¹, Péter Ádám

¹Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, Hungarian Academy of Sciences, P. O. Box 49, H-1525 Budapest, Hungary. szalay.viktor@wigner.mta.hu

The Journal of Chemical Physics

|August 18, 2012

Summary

A new variational finite basis representation/discrete variable representation (FBR/DVR) Hamiltonian operator was developed. This method enhances accuracy for quantum mechanical calculations by optimizing grid points and incorporating symmetry properties.

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Last Updated: May 19, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum mechanics
Computational chemistry
Theoretical physics

Background:

The finite basis representation/discrete variable representation (FBR/DVR) method is a powerful tool for solving quantum mechanical problems.
Accurate representation of the Hamiltonian operator is crucial for obtaining reliable results.
Existing FBR/DVR methods may have limitations in terms of accuracy and applicability to certain systems.

Purpose of the Study:

To introduce a novel variational finite basis representation/discrete variable representation (FBR/DVR) Hamiltonian operator.
To analyze the properties and optimize the performance of the proposed variational FBR/DVR method.
To demonstrate the applicability of the method to various quantum systems, including periodic ones.

Main Methods:

Development of a variational FBR/DVR Hamiltonian operator.
Exact calculation of matrix elements.
Diagonalization of commuting variational basis representations of coordinate operators.
Analysis of symmetry properties and incorporation into calculations.
Exploitation of quasi-Hermiticity for variational effective operators.

Main Results:

The introduced operator yields either a variational FBR or DVR depending on the basis set choice.
The domain of variational grid points is identified as subsets of points obtained from diagonalizing commuting operators.
The optimal subset of points for highest accuracy corresponds to the DVR with the smallest trace.
Symmetry properties are analyzed, and methods for their incorporation are discussed.
Fourier-basis FBR/DVR for periodic systems is derived within the presented theory.

Conclusions:

The developed variational FBR/DVR Hamiltonian operator offers enhanced accuracy and flexibility.
The method provides a systematic way to optimize grid points for improved computational efficiency.
The incorporation of symmetry and applicability to periodic systems broaden the scope of FBR/DVR methods.