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Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization

Scalable Nanohelices for Predictive Studies and Enhanced 3D Visualization

Published on: November 12, 2014

Accurate complex scaling of three dimensional numerical potentials.

Alessandro Cerioni¹, Luigi Genovese, Ivan Duchemin

¹European Synchrotron Radiation Facility, 6 rue Horowitz, BP220 38043 Grenoble Cedex 9, France. alessandro.cerioni@esrf.fr

The Journal of Chemical Physics

|June 8, 2013

Summary

Complex scaling in quantum mechanics can now be efficiently implemented using Daubechies wavelets on discrete grids. This novel wavelet-based approach offers high accuracy and generality for computing resonant states without artificial parameters.

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Area of Science:

Quantum Mechanics
Computational Physics
Non-Hermitian Systems

Background:

Complex scaling is a standard method for calculating resonant states of the Schrödinger operator.
Applying complex scaling to discrete numerical grids typically involves similarity transformations of the Hamiltonian.

Purpose of the Study:

To implement complex scaling for resonant state computations on discrete numerical grids.
To demonstrate the effectiveness of the Daubechies wavelet basis for this implementation.

Main Methods:

Utilized the Daubechies wavelet basis set for implementing complex scaling.
Applied a similarity transformation to the unscaled Hamiltonian on the discrete grid.
Performed complex scaling on three-dimensional numerical potentials.

Main Results:

The wavelet-based complex scaling approach is general and highly accurate.
This method eliminates the need for artificial convergence parameters.
Efficient and accurate complex scaling of three-dimensional potentials was achieved.

Conclusions:

The Daubechies wavelet basis provides a powerful and efficient tool for complex scaling in quantum mechanics.
This approach opens new avenues for computational studies in non-Hermitian quantum mechanics.
The method is suitable for investigating resonances in physical systems defined on discrete grids.