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Zinc sulphide
Published in D R Vij, Handbook of Electroluminescent Materials, 2004
Nigel Shepherd, Paul H Holloway
for a multi-particle system. Here H^ is the Hamiltonian operator and E is the total energy of the system. The Hamiltonian reflects all the electron–nuclei (attractive), electron–electron and nucleus–nucleus (repulsive) interactions. It is the sum of kinetic energy operators for the nuclei and the electrons, and the potential energy terms which represent the various coulombic interactions. It must also reflect the influence of external electric or magnetic fields. In short, the Hamiltonian must contain all the interactions which shift, or split the electron energy levels. Therefore, to solve the Schrödinger equation one must (a) set up the Hamiltonian matrix and (b) perform diagonalization of the Hamiltonian matrix to obtain the eigenvalues, or allowed energy level positions.
Design and Manufacturing of CNT-Based Nanodevices for Optical Sensing Applications
Published in Iniewski Krzysztof, Integrated Microsystems, 2017
Ning Xi, King Wai Chiu Lai, Jiangbo Zhang, Carmen Kar Man Fung, Hongzhi Chen, T. J. Tarn
First, we considered the electrical current model of a CNT. An electron transmission model calculated from the self-consistence nonequilibrium Green’s functions (NEGFs) method gives the optimal estimation of the current–voltage characteristic of a specific device; it is utilized as the state-space model for breakdown current control [78]. The quantum energy states and electron wave function inside the CNT can be modeled by the Hamiltonian matrix (H) which is derived from Schrodinger’s equation. The numerical solution of electron transport model for CNT conduction can be obtained by iteratively solving the NEGF formulas and Poisson’s equation as shown in Figure 18.14.
Computational study of cold ions trapped in a double-well potential
Published in Molecular Physics, 2019
Dmytro Shyshlov, Dmitri Babikov
The goal of our paper is to understand this interesting result by modelling the quantum dynamics of the system of two ions in the double-well potential as accurately as possible, without making any assumptions concerning the coupling strength or the energy spectrum of the double-well system. Such rigorous theoretical tools, including construction of the potential energy surface of the system and normal mode analysis, are often used by molecular physicists [21,22]. First, we consider an accurate potential energy surface of the system, without a Taylor series expansion of the Coulomb interaction, and without truncating any higher-order terms. Then we numerically search for the minimum energy point on the surface and perform the normal mode analysis. We avoid harmonic approximation and use the normal mode frequencies only to set up an efficient basis set for accurate representation of the wave function. Then we compute and numerically diagonalise the Hamiltonian matrix to determine accurate eigenstates of the system (energies and wave functions). These eigenstates are used to study evolution of the vibrational wave packets in time and space. Initial conditions are choosen to mimic the experiments conducted at NIST and Innsbruck [19,20].
A comparison of the scalar Hermitian product versus the complex product for obtaining electron densities and Fukui functions from complex wavefunctions for the temporary anion resonance states of Be−, Mg− and Ca−
Published in Molecular Physics, 2019
The are configurations obtained as the symmetrised linear combinations of Slater determinants. This produces a Hamiltonian matrix over configuration space that is complex symmetric, non-Hermitian.
The one-dimensional hydrogenic impurity states confined at one end of the InAs quantum well
Published in Philosophical Magazine, 2022
De-hua Wang, Xue He, Xue Liu, Bin-hua Chu, Wei Liu, Meng-meng Jiao
According to the effective mass approximation, the eigen-energies and eigen-functions of the 1-D hydrogenic impurity states confined at one end of the InAs quantum well have been obtained. Firstly, we use the traditional quantum mechanical method to get the analytical formula for the eigen-energy and eigen-function of this system by solving the Schrodinger equation exactly. It is found when the eigen-energy is negative, the eigen-wave function can be expressed as a Kummer function; however, when the eigen-energy is positive, the eigen-wave function exhibits the form of a Coulomb scattering function. Second, we use the linear variational method to obtain the approximate results of this system. We divide the Hamiltonian of the confined 1-D hydrogenic impurity into two parts: One part is the Hamiltonian of the particle in the infinite quantum well without impurity, and another part is the interaction potential of the electron and the impurity, which can be considered as a perturbation. Since the eigen-wave functions of the particle in the infinitely deep quantum well are well known and constitute an orthogonal normalised complete basis, then we can use this basis set to expand the wave function of the confined 1-D hydrogenic impurity state. By solving the Hamiltonian matrix equation, we get the numerical values of the eigen-energies and eigen-wave functions. It is found when the quantum well is very narrow, the eigen-energy approaches to the exact result with a small number of basis set functions; whereas for a relatively wide quantum well, it is necessary to use a large number of basis set functions. The confinement effect of the quantum well on the energy level and binding energy of the hydrogenic impurity state has been studied in great detail. The calculation results suggest, for the InAs quntum well, when the width of the well a < 10a0* = 335.93 nm, the confinement effect is very significant. Although the linear variational method used in this work has only been applied to the hydrgoenic impurity state confined in the quantum well, quantum dot or quantum wire, for the non-hydrgoenic confined systems, this method is still applicable. In view of this point, our work can guide the future research on the energy level of impurity state confined in the external environment and has some practical applications in semiconductor physics and material sciences.