Hamiltonian operator

Toward Selectively Toxic Silver Nanoparticles

Published in Huiliang Cao, Silver Nanoparticles for Antibacterial Devices, 2017

where H is the Hamiltonian operator, E is the total energy of the system and ψ is the wave function that depends on the positions and spins of the electrons. For studying the dynamics of electrons, the atomic nuclei are considered as fixed in space and surrounded by an ‘electron gas’. Based on the Born–Oppenheimer approximation, H is (Kohn 1999)

Exploring space-energy matching via quantum-molecular mechanics modeling and breakage dynamics-energy dissipation via microhydrodynamic modeling to improve the screening efficiency of nanosuspension prepared by wet media milling

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Journal Information

Published in Expert Opinion on Drug Delivery, 2021

Jing Tian, Fangxia Qiao, Yanhui Hou, Bin Tian, Jianhong Yang

where H is the Hamiltonian operator, Ψ is the wave function, E represents energy, r represents electrons, and R denotes the positions of the electrons relative to the atomic nucleus. Thereinto, the nucleus term was considered in the earliest equation, due to motions of electrons being actually affected by other electrons and nucleus. Subsequently, based on the theory of quantum mechanics methods, it removes the nucleus term from the R term and mainly the parts for electrons are derived. However, the difficulty of this computation increases greatly because of the additional dimension. The density functional theory must be applied to reduce the difficulty because it transforms the three-dimensional wave function equation into a three-dimensional density function [29].

Hamiltonian operator

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Toward Selectively Toxic Silver Nanoparticles

Exploring space-energy matching via quantum-molecular mechanics modeling and breakage dynamics-energy dissipation via microhydrodynamic modeling to improve the screening efficiency of nanosuspension prepared by wet media milling