Symmetric matrix methods for Schrodinger eigenvectors

Grieves, Brian; Dunn, Dennis

doi:10.1088/0305-4470/23/23/021

Cited by 11 publications

(1 citation statement)

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“…A highly successful approach for approximating the wave functions of 2D quantum problems is the Numerov method, , a numerical framework for solving ordinary differential equations of second order without first-order terms. Numerov’s method provides a general strategy to numerically solve Schrödinger’s equation and a variety of implementations for 1D systems have been derived. − The first extension to higher dimensions (2D and 3D) was reported by Graen and Grabmüller to study nuclear quantum effects . To increase the accuracy of the higher-dimensional implementation while reducing memory and computing demand, an adapted Numerov method was developed using sparse matrix algebra routines .…”

Section: Introductionmentioning

confidence: 99%

Sculpting the Unseen: Exploring Quantum Mechanics Using 3D-Printed Potential Surfaces and Wave Functions

Purtscher,

Schuler,

Hofer

2024

J. Chem. Educ.

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Due to its abstract and counterintuitive nature, quantum mechanics is considered as one of the most challenging subjects in science and technology. This study outlines a general workflow for the fabrication of quantum mechanical wave functions utilizing 3D-printing technology. The novel technique offers a more comprehensive and tangible way to visualize and understand complex quantum phenomena when compared to the standard approach of presenting 2D projections of the associated threedimensional mathematical objects. By using numerical approaches to solve the Schrodinger equation this approach can be applied to a broad range of potentials relevant to a number of different experimental techniques such as vibrational spectroscopy and quantum tunneling. By modifying the generated 3D models appropriately, without changing their overall descriptive character, further improvements in the representation of the underlying potential surface and the associated wave functions can be achieved. The correct vertical alignment of the potential surface and wave functions was further enhanced via a 3D-printed rack designed specifically for this project, which allowed the models to be displayed in the correct energetic order.

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