Electron’s Position Expectation Values and Energy Spectrum of Lithium Ion (Li^(2+)) on Principal Quantum Number n≤3

The purpose of this study is to determine the electron’s position expectation values and energy spectrum on the Li2+ ion on the principal quantum number n≤3. This research using literature study methods on quantum mechanics. The expectation values of the electron position and the energy spectrum of the Li2+ ion uses numerical calculations using the Matlab 2019a program. The steps in this research method include: preparation; theory development; simulation; validation of the results of theory development; results of theory development; discussion and conclusion. The results obtained in this study are the electron’s position expectation values and energy of the Lithium ion. The electron’s position expectation values indicates the presence of electrons that often appear around the x-axis by relying on the interval used. The larger the interval, the more constant the electron’s position expectation values will be and towards an almost constant value. From the analysis results, the expectation value varies in positions from 0,0001a0 to 0,1637a0. The electron energy spectrum of the Li2+ ion is inversely proportional to the square of the principal quantum number (n),E1= -122,4 eV ; E2= -30,6 eV ; E3= -13,6 eV

How to Calculate Condensed Matter Electronic Structure Based on Multi-Electron Atom Semi-Classical Model

Atoms are proved to be semi-classical electronic systems in the sense of closeness of their exact quantum electron energy spectrum with that calculated within semi-classical approximation. Introduced semi-classical model of atom represents the wave functions of bounded in atom electrons in form of hydrogen-like atomic orbitals with explicitly defined effective charge numbers. The hydrogen-like electron orbitals of constituting condensed matter atoms are used to calculate the matrix elements of the secular equation determining the condensed matter electronic structure in the linear-combination-of-atomic-orbitals (LCAO) approach. Preliminary test calculations are conducted for boron B atom and diboron B2 molecule electron systems.

MATLAB Wavelet analysis of electron energy spectrum in one-dimensional quantum well with infinitely high walls for Al-Ga-As system (0 < x < 1)

This paper presents calculations of electronic states in AlxGa1-x As semiconductor nanostructures and simulates the envelope wave functions of quantum energy levels in a one-dimensional quantum well with infinitely high walls of a given width at various values of x. For the analysis of results the authors choose the function wtmm from the Matlab library that fixes the extremums and which is a characteristic of the fractality of the envelope wave functions of quantum energy levels.

MATLAB Modelling electron energy spectrum in one-dimensional quantum well with infinitely high walls for GaAs solid solution

The paper presents calculations of electron states in semiconductor nanostructures AlxGa1–x As (x=0) and simulates the energy spectrum of the electron in a one-dimensional quantum well with infinitely high walls of a given width (from 10 to 30 atomic monolayers) using MATLAB application. The data is visualized using a wavelet transform with different wavelet functions.

Quantum field theory of space-like neutrino

We performed a Lorentz covariant quantization of the spin-1/2 fermion field assuming the space-like energy-momentum dispersion relation. We achieved the task in the following steps: (i) determining the unitary realizations of the inhomogenous Lorentz group in the preferred frame scenario by means of the Wigner–Mackey induction procedure and constructing the Fock space; (ii) formulating the theory in a manifestly covariant way by constructing the field amplitudes according to the Weinberg method; (iii) obtaining the final constraints on the amplitudes by postulating a Dirac-like free field equation. Our theory allows to predict all chiral properties of the neutrinos, preserving the Standard Model dynamics. We discussed the form of the fundamental observables, energy and helicity, and show that non-observation of the $$+\tfrac{1}{2}$$ + 1 2 helicity state of the neutrino and the $$-\tfrac{1}{2}$$ - 1 2 helicity state of the antineutrino could be a direct consequence of the “tachyoneity” of neutrinos at the free level. We found that the free field theory of the space-like neutrino is not invariant under the C and P transformations separately but is CP-invariant. We calculated and analyzed the electron energy spectrum in tritium decay within the framework of our theory and found an excellent agreement with the recent measurement of KATRIN. In our formalism the questions of negative/imaginary energies and the causality problem does not appear.

Energy Levels in Nanowires and Nanorods with a Finite Potential Well

The energy of electrons and holes in cylindrical quantum wires with a finite potential well was calculated by two methods. An analytical expression is approximately determined that allows one to calculate the energy of electrons and holes at the first discrete level in a cylindrical quantum wire. The electron energy was calculated by two methods for cylindrical layers of different radius. In the calculations, the nonparabolicity of the electron energy spectrum is taken into account. The dependence of the effective masses of electrons and holes on the radius of a quantum wires is determined. An analysis is made of the dependence of the energy of electrons and holes on the internal and external radii, and it is determined that the energy of electrons and holes in cylindrical layers with a constant thickness weakly depends on the internal radius. The results were obtained for the InP/InAs heterostructures.