Quantum Mechanical Description Of Electrons Research Articles

Treating disorder in introductory solid state physics

Introductory textbooks in solid state physics present solvable models for illustrating the occurrence of allowed bands and forbidden gaps in the energy spectrum of Bloch electrons. However, the quantum mechanical description of electrons in non-periodic solids, such as amorphous materials, is beyond the scope of introductory courses because of its intrinsic complexity. The tight-binding approximation can account for such a scenario by letting the atomic levels vary at random from lattice site to site. We theoretically tackle the study of the average properties of the energy spectrum by introducing a transfer matrix method that allows us to obtain closed expressions for the so-called coherent potential. The coherent potential is energy-dependent and constant in space. It replaces the actual atomic random potential, thus generating a periodic effective medium with the same average properties as the non-periodic solid. We demonstrate that the average density of states can be calculated within this framework without relying on heavy mathematical machinery. Thus, our approach is suitable for introductory courses in solid state physics and materials science.

Improving the Accuracy of Atomistic Simulations of the Electrochemical Interface.

Atomistic simulation of the electrochemical double layer is an ambitious undertaking, requiring quantum mechanical description of electrons, phase space sampling of liquid electrolytes, and equilibration of electrolytes over nanosecond time scales. All models of electrochemistry make different trade-offs in the approximation of electrons and atomic configurations, from the extremes of classical molecular dynamics of a complete interface with point-charge atoms to correlated electronic structure methods of a single electrode configuration with no dynamics or electrolyte. Here, we review the spectrum of simulation techniques suitable for electrochemistry, focusing on the key approximations and accuracy considerations for each technique. We discuss promising approaches, such as enhanced sampling techniques for atomic configurations and computationally efficient beyond density functional theory (DFT) electronic methods, that will push electrochemical simulations beyond the present frontier.

A quantum mechanical analysis of Smith–Purcell free-electron lasers

The paper presents a quantum mechanical treatment for analyzing the Smith–Purcell radiation generated by charged particles passing over a periodic conducting structure. In our theoretical model, the electrons interact with a surface harmonic wave excited near the diffraction grating when the electron velocity is almost equal to the phase velocity of the surface wave. Then, the surface harmonic wave is electromagnetically coupled to a radiation mode. The dynamics of electrons are analyzed quantum mechanically where the electron is represented as a traveling electron wave with a finite spreading length. The conversion of the surface wave into a propagating mode is analyzed using the classical Maxwell׳s equations. In the small-signal gain regime, closed-form expressions for the contributions of the stimulated and spontaneous emissions to the evolution of the surface wave are derived. The inclusion of the spreading length of the electron wave to the emission spectral line is investigated. Finally, we compare our results based on the quantum mechanical description of electron and those based on the classical approach where a good agreement is confirmed.

Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation

We elaborate on the theory for the variational solution of the Schrödinger equation of small atomic and molecular systems without relying on the Born-Oppenheimer paradigm. The all-particle Schrödinger equation is solved in a numerical procedure using the variational principle, Cartesian coordinates, parameterized explicitly correlated Gaussian functions with polynomial prefactors, and the global vector representation. As a result, non-relativistic energy levels and wave functions of few-particle systems can be obtained for various angular momentum, parity, and spin quantum numbers. A stochastic variational optimization of the basis function parameters facilitates the calculation of accurate energies and wave functions for the ground and some excited rotational-(vibrational-)electronic states of H(2) (+) and H(2), three bound states of the positronium molecule, Ps(2), and the ground and two excited states of the (7)Li atom.

Particle-in-a-Box Dynamics

This SymMath activity provides a simple example of a quantum mechanical description of electron or exciton motion designed for use in junior�senior level quantum chemistry courses.

Dissecting hydrophobicity

The perceived phobia (fear) of some apolar substances for aqueous (hydro) environments does not imply lack of attraction to water. Rather, it originates from the strength of this attraction, which, similar to that between the constituents of apolar substances, is smaller than the force between water molecules. Fear of those who dominate the scene (in this case, water hydrogen bonds) is hardly surprising. The concept of hydrophobicity, intuitively associated with the demixing of oil and water, appears in most biophysics and biochemistry textbooks, and it is generally accepted that hydrophobic interactions are a major driving force of fundamental biological processes, for example, protein folding, molecular recognition, and the formation of membranes (1,2). Yet, the molecular theory of the hydrophobic effect and the microscopic understanding of the hydration of hydrophobic species (or hydrophobic hydration), are incomplete. The article by Li et al. (3) in this issue of PNAS presents the first investigation of hydrophobic association for a model system (two methane molecules in water) entirely based on first principles, i.e., on a quantum mechanical description of electronic and electron–ion interactions (4) of the combined solute–solvent system. The potential of mean force between the two methane molecules computed in ref. 3 is consistent with the data extracted from several hydrocarbon solubility experiments, but it is substantially different from what is found in simulations based on empirical classical force fields. These simulations represent the majority of computer simulations carried out in the last 30 years to investigate hydrophobic effects at the microscopic level. The results of ref. 3 indicate that these empirical simulations may lead to an underestimation of the hydrophobic effect in many instances, and they point to the need for an accurate, ab …

On the description of electrons on a noncommutative plane threaded by a transversal magnetic field

In this paper we deal with the quantum-mechanical description of electrons on a noncommutative plane under the influence of a transversal and homogeneous magnetic field. For this purpose the noncommutativity has been implemented by resorting to the quantum Euclidean space relying on the quantum group SOq(N) and to the so-called noncommutative θ-formulation, which is familiar in string theory. Matching conditions have been established and discussed.