Related papers: Embedding on to a one-dimensional crystal
In this article we discuss a procedure to solve the one dimensional (1D) Schroedinger Equation for a periodic potential, which may be well suited to teach band structure theory. The procedure is conceptually very simple, so that it may be…
Without our ability to model and manipulate the band structure of semiconducting materials, the modern digital computer would be impractically large, hot, and expensive. In the undergraduate QM curriculum, we studied the effect of spatially…
A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta…
A new method for finding electronic structure and wavefunctions of electrons in quasiperiodic potential is introduced. To obtain results it uses slightly modified Schrodinger equation in spaces of dimensionality higher than physical space.…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
In this study, the Schrodinger equation of a valence electron in a periodic crystal potential is formulated and solved using the elliptic function formalism. The method allows double periodic lattice planes to be represented in the Gauss…
We show how arbitrary unit cells of periodic materials can be represented as graphs whose nodes represent atoms and whose weighted edges represent tunneling connections between atoms. Further, we present methods to calculate the band…
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…
We report on a theoreticl study of the electronic structure of quasiperiodic, quasi-one-dimensional systems where fully three dimensional interaction potentials are taken into account. In our approach, the actual physical potential acting…
A prototypical model of a one-dimensional metallic monatomic solid containing noninteracting electrons is studied, where the argument of the cosine potential energy periodic with the lattice contains the first reciprocal lattice vector G1 =…
We introduce a practical and efficient approach for calculating the all-electron full potential bandstructure in real space, employing a finite element basis. As an alternative to the k-space method, the method involves the self-consistent…
In this paper, a new method based on Greens function theory and Fourier transform analysis has been proposed for calculating band structure with high accuracy and low processing time. This method utilizes sampling of potential energy in…
We investigate the fractional Schr\"odinger equation with a periodic $\mathcal{PT}$-symmetric potential. In the inverse space, the problem transfers into a first-order nonlocal frequency-delay partial differential equation. We show that at…
An embedding method for solving the time-dependent Schr\"odinger equation is developed using the Dirac-Frenkel variational principle. Embedding allows the time-evolution of the wavefunction to be calculated explicitly in a limited region of…
We extend density matrix embedding theory to periodic systems, resulting in an electronic band structure method for solid-state materials. The electron correlation can be captured by means of a local impurity model using various choices of…
Constructing a quantum description of crystals from scattering experiments is of paramount importance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab-initio models. While reconstruction methods of…
In the one-dimensional periodic potential case, we formulate the condition of Bloch periodicity for the reduced action by using the relation between the wave function and the reduced action established in the context of the equivalence…
The relation between the Poisson and Schr\"odinger equation in one dimension is obtained through a simple transformation. It is pointed out that this analogy between both equations can be only applied for potentials that involve a…
Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar…
Following two recent papers [Phys. Chem. Chem. Phys. 2015, \textbf{17}, 3196; Mol. Phys. 2015, \textbf{113}, 1843], we perform a larger-scale study of chemical structure in one dimension (1D). We identify a wide, and occasionally…