Path Integral Quantum Mechanics and Molecular Dynamics - Maple Application Center
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Path Integral Quantum Mechanics and Molecular Dynamics

: Kuntal Ghosh
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Quantum mechanics is crucial to the understanding of the way nature works. Traditionally, quantum mechanics is formulated in terms of the wave function, proposed by Schrödinger. It is this wave function which carries all the information about the system under consideration, and is deduced from Schrödinger's equation. Alternatively, quantum mechanics can also be formulated in terms of the wave vector, using the Dirac notation. In fact, there are nine different formulations of quantum mechanics. One of the most fundamental as well as strikingly beautiful formulations of quantum mechanics is Feynman's path integral. This worksheet explores a few fundamental concepts of path integrals, with special emphasis on the harmonic oscillator model. Path integral calculations are often carried out in the framework of molecular dynamics (MD) simulations, popularly called Path Integral Molecular Dynamics (PIMD). PIMD simulations are critically important to capture nuclear quantum effects (NQEs) in atomistic simulations, simply because most MD methods treat the nuclei classically, even if the electronic motion is treated quantum mechanically. PIMD, due to its very construction, effectively does away with this issue. This worksheet also gives a brief introduction to PIMD with a simple numerical illustration using the harmonic oscillator model. This worksheet uses the Maple Quantum Chemistry Toolbox.

Application Details

Publish Date: March 14, 2022
Created In: Maple 2021
Language: English

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