Energy Wave Functions Research Articles

Anisotropy of the Magnetic Properties of Er³⁺ Ion in Erbium Iron Garnet Crystal at Low Temperature

With the consideration of crystal field (CF) and exchange interaction between the magnetic ions, we conduct a theoretical analysis to the anisotropy of the magnetization caused by Er^3+ ions in erbium iron garnet (ErIG) in the temperature range from 4.2 to 150 K. It is found that the anisotropy of the magnetization caused by Er^3+ ions originates mainly from the anisotropic Er^3+–Fe^3+ ion exchange interaction. In the course of research, a set of relatively suitable CF parameters are obtained by analyzing the influence of different CF parameters on the magnetization. The secular equation is solved by quantum theory after taking into account the coupling of the ⁴I_15/2 and ⁴I_13/2 multiplets, and the energy levels and wave functions of Er^3+ ions are further obtained. Then, the magnetization of Er^3+ ions at six inequivalent sublattices when magnetized along the [100], [110], and [111] directions are calculated, respectively. Following this, comparisons between the average value of the so-obtained six quantities and the experimental data are made in the [100], [110], and [111] magnetization directions. The calculated results coincide well with the experimental data and [100] is the easy magnetization direction.

In-plane transition metal dichalcogenide quantum wells: Effective Hamiltonian approach

In-plane or Lateral two dimensional (2D) heterostructures, due to its unique optical and transport properties as well as junction feature, are becoming a good candidate for future electronics and photonics devices. In particular, lateral stitched heterostructures of MoS2/WSe2 mostly synthesized by lithographic pattern provides type II band alignment therefore, the possibility of forming a type II lateral quantum well may be considered as a serious research topic. Here, We theoretically obtain energy levels and electron and hole wave functions in a lateral MoS2/WSe2 single and double quantum well (LSQW and LDQW) which is evidenced by experiments. Within effective 2D Dirac Hamiltonian, an analytical expression for energy dispersion in growth direction has been derived. Based on numerical approach, the variation of energy levels, wave function and number of allowed energy levels as a function of the width of the quantum well are discussed for single electron and hole. We observed that by increasing QW the number of energy levels increases similar to conventional semiconductor QW, but surprising behavior is in LSQW of WSe2/MoS2/WSe2 that the number of allowed energy levels inside QW increases by increasing well width. Our study paves the way for the implementation of in-plane quantum wells in electronic and optoelectronic devices such as sensors, detectors and solar cells.

α−α correlations in nuclei above the doubly-magic Pb208 nucleus

The properties of the $^{216}\mathrm{Rn}$ nucleus have been investigated using $\ensuremath{\alpha}\text{\ensuremath{-}}^{212}\mathrm{Po}$ and $^{8}\mathrm{Be}\text{\ensuremath{-}}^{208}\mathrm{Pb}$ systems with each interacting via a cluster model local interaction, and with a three-body $\ensuremath{\alpha}\text{\ensuremath{-}}\ensuremath{\alpha}\text{\ensuremath{-}}^{208}\mathrm{Pb}$ system within the coupled-channel formalism. The energies, transition probabilities, and cluster decay half-lives are compared with available experimental data. The two-body configurations are found to yield similar results, in fair agreement with the existing experimental data. The three-body system yields energy spectra and wave functions whose lowest energy states provides satisfactory and better description of the nucleus.

Ab initio Morse/long-range potential energy functions plus spectroscopic and thermophysical properties of heteronuclear diatomic complexes of xenon with the rare gases

New interatomic potential energy curves of xenon-helium (Xe-He), xenon-neon (Xe-Ne), and xenon-argon (Xe-Ar) atom pairs are developed by state-of-the-art ab initio calculations. Coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)] is used to calculate the majority of the interaction between atoms, on (multiple) augmented correlation-consistent basis sets for valence orbitals, extrapolated to the complete basis set (CBS) limit. Contributions from inner nuclear electronic correlation, relativistic effects, and higher-order excitations beyond CCSD(T) are also considered as corrections. For each system, an analytical Morse/long-range (MLR) potential functions, is fitted to 32 ab initio data using only 13 parameters: the poorest-quality fit yielded a dimensionless-root-mean-square-deviation (dd¯) of only 1.51. The ro-vibrational energy levels and wave functions, resonance states, effective radial potential energy curves, absorption spectra and thermophysical properties have also been computed.

High harmonic generation spectra for lithium embedded in plasma environment

Effect of plasma on High harmonic generation of Lithium is investigated. Variation of the strength of different harmonics with respect to changes in Debye length is shown. The unperturbed energy eigenvalues and wavefunctions are calculated using the pseudostate summation technique while for the time evolution of wavefunctions the symplectic method is applied. Results for the numerical simulation of High harmonic generation spectra for plasma embedded Lithium are reported.

Influence of External Magnetic and Aharanov-Bohm (AB) Fields on the Energy Spectra of the Modified Kratzer plus Screened Coulomb Potential

In this article, the modified Kratzer plus screened Coulomb potential is scrutinized taking into consideration the effects of magnetic and AB flux fields within the non-relativistic regime using the Nikiforov-Uvarov-Functional Analysis method (NUFA) method. The energy equation and wave function of the system are obtained in close form. We find that the totality of effects these fields result in removal of degeneracy and raising the bound state energy of the system. More so, it could be concluded that to control the energy spectra of this system, the AB-flux and magnetic field will do so greatly. The results from this study can be applied in condensed matter physics, atomic and molecular physics.

Regulation of optical properties by applied external fields for a quantum well with Hulthen potential

In this present study, the effects of electric, magnetic, and non-resonant intense laser field (ILF) on the linear, third-order nonlinear, and total optical absorption coefficients (TOACs) and relative refractive index changes (RRICs) of GaAs quantum well, having Hulthen confinement potential, were theoretically investigated. In addition, the dependence of the nonlinear optical properties in the structure on the optical intensity of incident photon and the inverse relaxation time was also calculated. To do this research, firstly the energy eigenvalues and eigenfunctions of the structure were calculated by using the effective mass and envelope function approaches. By using these calculated subband energy levels and wave functions belonging to these levels, the nonlinear optical properties of the system were obtained via the iterative method, within the compact density matrix approach framework. The obtained numerical results show that the optical properties of the considered system depend on the externally applied fields. With the applied external electric and magnetic field, the peak positions of TOACs and RRICs shift to higher energies, and the peak magnitudes increase. The high-frequency ILF applied to the structure shifts the peak positions of TOACs and RRICs initially towards higher energies and then towards lower energies and their peak sizes increase. These results show that the optical properties of the system can be adjusted purposively by changing the magnitude of applied external fields.

Terahertz laser field manipulation on the electronic and nonlinear optical properties of laterally-coupled quantum well wires.

An intense terahertz laser field is shown to actively manipulate the electronic states, as well as the linear and nonlinear optical absorption coefficients, of the laterally-coupled quantum well wires (LCQWWs). The laser-dressed quantum states of the LCQWWs are achieved using the non-perturbative Floquet method and the two-dimensional diagonalization technique under the effective mass approximation. We have demonstrated that the intense terahertz laser field induces a strong deformation of the confinement potential configuration of the LCQWWs, thus pronouncedly dressing the energy levels and wave functions. An unambiguous picture is depicted for the evolution of the laser-dressed quantum states with the increase of the laser-dressed parameter characterizing the strength of the laser-dressed effect. On this basis, the resonant peak positions of the linear and nonlinear optical absorption coefficients feature a blue shift followed by a red shift with an increase of the laser-dressed parameter. Furthermore, the evolution of the peak values for the linear and third-order nonlinear optical absorption coefficients as a function of the laser-dressed parameter is comprehensively discussed. Moreover, in contrast to the case without intense terahertz laser field, the peak values of the linear, third-order nonlinear, and total optical absorption coefficients can be obviously enhanced at the same frequency position by manipulating the appropriate laser-dressed parameter. A similar feature can be found in the linear, third-order nonlinear, and total refractive index changes. Our findings are conducive to the implementation of the expected quantum states and nonlinear optical effects in the LCQWWs, paving the way for new designs in tunable optical switches, infrared photo-detectors and infrared modulators.

Electronic and optical properties of cubic quantum dots subjected to terahertz laser field

This study introduces the influence of linearly polarized terahertz laser field (TLF) on electronic and anisotropic optical absorption coefficients (OACs) related to the cubical quantum dots (CQDs). The energy levels and wave functions of the system are obtained by solving the Schrödinger equation within the framework of the effective-mass. The OACs are inferred from the scheme of compact density-matrix formalism. The results show that the laser correction parameters and polarization angle of TLF have a significant influence on the optical properties. As a key result, the modulation of anisotropic OACs of CQDs by terahertz laser field with different parameters is given.

A Non-relativistic Approach to Relativistic Quantum Mechanics: The Case of the Harmonic Oscillator

A recently proposed approach to relativistic quantum mechanics (Grave de Peralta, Poveda, Poirier in Eur J Phys 42:055404, 2021) is applied to the problem of a particle in a quadratic potential. The methods, both exact and approximate, allow one to obtain eigenstate energy levels and wavefunctions, using conventional numerical eigensolvers applied to Schrödinger-like equations. Results are obtained over a nine-order-of-magnitude variation of system parameters, ranging from the non-relativistic to the ultrarelativistic limits. Various trends are analyzed and discussed—some of which might have been easily predicted, others which may be a bit more surprising.

Investigation of two-electron quantum dot in a magnetic field by using of quasi-exact-solvable method

We study the non-relativistic particles of a two dimensional two-electron quantum dot. We consider the system in the presence of harmonic plus linear terms as well as a term related to spin interaction. The solution of the system is obtained by using of Quasi-Exactly-Solvable (QES) method. Next, we calculate the energy eigenstates and wave functions of the system in the presence of an external magnetic field.

Exact solution of the semiconfined harmonic oscillator model with a position-dependent effective mass in an external homogeneous field

We extend exactly solvable model of a one-dimensional non-relativistic canonical semiconfined quantum harmonic oscillator with a mass that varies with position to the case where an external homogeneous field is applied. The problem is still exactly solvable and the analytic expression of the wave functions of the stationary states is expressed by means of generalised Laguerre polynomials, too. Unlike the case without any external field, when the energy spectrum completely overlaps with the energy spectrum of the standard non-relativistic canonical quantum harmonic oscillator, the energy spectrum is now still equidistant but depends on the semiconfinement parameter a. We also compute probabilities of the transitions for the model under the external field and discuss limit cases for the energy spectrum, wave functions and probabilities of transitions, when the semiconfinement parameter a goes to infinity.

Cover Feature: Development and Application of a Complete Active Space Spin‐Orbit Configuration Interaction Program Designed for Single Molecule Magnets (ChemPhysChem 1/2022)

The Cover Feature illustrates how magnetic data of powder samples of oligonuclear transition metal complexes can be simulated and analysed from ab initio energy levels and wave functions obtained by spin orbit configuration interaction. More information can be found in the Article by Bodenstein, Heimermann, Fink, and van Wüllen.

Thermodynamic properties of GaAs quantum dot confined by asymmetric Gaussian potential

In the present work, we have calculated the thermodynamic properties of an asymmetrical Gaussian potential quantum dot under external electric field. To this end, we have solved the Schr�dinger equation and have obtained the energy levels and wave functions, analytically. According to the obtained eigenvalues, we have calculated the partition function of the system by the Poisson summation formalism. Afterward, we have deduced some thermodynamic properties such as mean energy, entropy, specific heat and free energy under the application of an external electric field using the canonical ensemble approach. These thermodynamic properties for an asymmetrical Gaussian potential GaAs quantum dot have been discussed in detail.

Optical gain analysis of GaInP/AlGaInP nanoscale heterostructure for applications in visible light emission

In quantum well structures, charge carriers are confined in the well region and barrier region due to the discontinuity in the bandgap and larger built-in potential. Thus, for a smaller current, we can have a higher gain. This work reports the energy wavefunction and optical gain analysis of the GaAs-based quantum well structure made of GaInP/AlGaInP material layers. The structure is also examinedsubject to the effect of external pressure and temperature to study the tunability. The designed structure shows stability near the room temperature. The 6 × 6 Hamiltonian matrix is solved and the Luttinger-Kohn model with the conduction band is used for the calculation of band structure. In the quantum well structure, the thickness of the active layers is in our control. This is an important advantage for device fabrication. The material and the size of the layers are selected on the basis of their suitability to generate the radiation in the range of the red spectrum (620-–750 nm).The designed QW heterostructure is thus found to be suitable for photodynamic treatment (PDT) and dermatological treatments.

First-Principles Study of Optical Absorption Energies, Ligand Field and Spin-Hamiltonian Parameters of Cr3+ Ions in Emeralds.

Herein, we study the electronic structure, energies, and vibronic structure of optical d-d transitions of Cr3+ ions doped in beryl (Be3Si6Al2O18:Cr3+, emerald). A computational protocol is developed that combines periodic density functional theory (for modeling of the bulk crystalline lattice of emerald) and the multireference configuration interaction complete active space self-consistent field method supplemented with n-electron valence second-order perturbation theory (for the calculation of the energy levels, wave functions, and spin-Hamiltonian and ligand-field parameters of the trigonal Cr3+ centers in the [CrO6]9- clusters embedded in an extended point charge field). Ligand-field parameters were extracted from mapping the effective ligand-field Hamiltonian onto the full many-particle Hamiltonian from one side and from a direct fit to energies of computed d-d transitions on the other side. These have been analyzed using ab initio ligand-field theory. The quality of the theoretical predictions is critically assessed through a detailed comparison with the available experimental data.

Near-infrared range tuneability in GaAs-based type-II nanoscale heterostructure emitter

We present the investigation of energy wavefunctions, dispersion profile, dipole momentum behavior, and optical gain for a nanoscale heterostructure formed with material layers of InAlAs/InGaAs/GaAsSb/InGaAs/InAlAs on a GaAs substrate. The designed structure is simulated with a 6 band k p formalism for the investigation. At room temperature, the 1548-nm wavelength has an optical gain of 2352/cm, making it suitable for NIR applications. The response of the designed heterostructure is also investigated with external temperature, strain, charge density, and electric field variations to report the tunability of the optical gain and wavelength. Due to its tunability in the NIR wavelength region, this structure can be used for different NIR applications without changing the material system.

The investigation of Carnot engine in the presence of deformed formalism

In this paper, after introducing a kind of [Formula: see text]-deformation in quantum mechanics, first [Formula: see text]-deformed form of Schrödinger equation for a single particle in a box is derived. Then, the energy eigenvalues and wave function in Schrödinger equation are studied. Also, we discuss the Carnot cycle by using of the energy eigenvalues. We obtain the thermodynamic properties such as force, heat transferred, work done and efficiency in the cycle. Finally, all results have satisfied what we had expected before.

Two-body Wigner molecularization in asymmetric quantum dot spin qubits

Coulomb interactions strongly influence the energy spectrum and wave functions of few electrons or holes in single quantum dots. Indeed, for weak confinement potentials, the Coulomb repulsion splits apart the particles, leading to the formation of Wigner molecules. Here, the authors discuss how the confinement anisotropy favors the molecularization and compare the impact on readout and exchange interactions for spin qubits in different semiconductor materials.

On the position-dependent mass Schrödinger equation for Mie-type potentials

The exactly solvable Position Dependent Mass Schrödinger Equation (PDMSE) for Mie-type potentials is presented. To that, by means of a point canonical transformation the exactly solvable constant mass Schrödinger equation is transformed into a PDMSE. The mapping between both Schrödinger equations lets obtain the energy spectra and wave functions for the potential under study. This happens for any selection of the O von Roos ambiguity parameters involved in the kinetic energy operator. The exactly solvable multiparameter exponential-type potential for the constant mass Schrödinger equation constitutes the reference problem allowing to solve the PDMSE for Mie potentials and mass functions of the form given by m(x) = skx s-1/(xs + 1))2. Thereby, as a useful application of our proposal, the particular Lennard-Jones potential is presented as an example of Mie potential by considering the mass distribution m(x) = 6kx 5/(x 6 + 1))2. The proposed method is general and can be straightforwardly applied to the solution of the PDMSE for other potential models and/or with different position-dependent mass distributions.