Energy levels of a two-dimensional anharmonic oscillator: Hill determinant approach

Pramana ◽  
1993 ◽  
Vol 41 (6) ◽  
pp. 493-502 ◽  
Author(s):  
M R M Witwit
Keyword(s):  
Anharmonic Oscillator ◽  
Energy Levels ◽  
Two Dimensional

scholarly journals On the noncommutative energy level in a two-dimensional anharmonic oscillatoric Oscillator

2019 ◽  
Vol 65 (4 Jul-Aug) ◽  
pp. 398
Author(s):  
G. Farías ◽  
E.A. Mena Barboza ◽  
And S. Rodríguez
Keyword(s):  
Energy Level ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
Two Dimensional ◽  
Quantum Properties ◽  
Perturbation Term

We study quantum properties of a two-dimensional anharmonic oscillator in the space-space and momentum-momentum in noncommutative variables. This work show ex- plicitly the effects of both deformations in the energy levels. The perturbation term in the Hamiltonian manifest the main difference of the noncommutative parameters. Particular nu- merical values of noncommutative parameters are examined and graphically illustrated for different nx and ny non-negative integers.

scholarly journals The influence of Coulomb interaction screening on the excitons in disordered two-dimensional insulators

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
E. V. Kirichenko ◽  
V. A. Stephanovich
Keyword(s):  
Coulomb Interaction ◽  
Energy Levels ◽  
Transition Metal Dichalcogenides ◽  
Extreme Case ◽  
Bound State ◽  
Joint Effect ◽  
Two Dimensional ◽  
Inorganic Substances ◽  
Metal Dichalcogenides ◽  
Interaction Screening

AbstractWe study the joint effect of disorder and Coulomb interaction screening on the exciton spectra in two-dimensional (2D) structures. These can be van der Waals structures or heterostructures of organic (polymeric) semiconductors as well as inorganic substances like transition metal dichalcogenides. We consider 2D screened hydrogenic problem with Rytova–Keldysh interaction by means of so-called fractional Scrödinger equation. Our main finding is that above synergy between screening and disorder either destroys the exciton (strong screening) or promote the creation of a bound state, leading to its collapse in the extreme case. Our second finding is energy levels crossing, i.e. the degeneracy (with respect to index $$\mu $$ μ ) of the exciton eigenenergies at certain discrete value of screening radius. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in above 2D semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important.

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

scholarly journals Ultrabroadband two-dimensional electronic spectroscopy reveals energy flow pathways in LHCII across the visible spectrum

2019 ◽  
Vol 205 ◽  
pp. 09034
Author(s):  
Minjung Son ◽  
Alberta Pinnola ◽  
Roberto Bassi ◽  
Gabriela S. Schlau-Cohen
Keyword(s):  
Energy Transfer ◽  
Excited States ◽  
Energy Flow ◽  
Energy Levels ◽  
Electronic Spectroscopy ◽  
Visible Region ◽  
Visible Spectrum ◽  
Energy Relaxation ◽  
Two Dimensional ◽  
Flow Pathways

We utilise ultrabroadband two-dimensional electronic spectroscopy to map out pathways of energy flow in LHCII across the entire visible region. In addition to the well-established, low-lying chlorophyll Qy bands, our results reveal additional pathways of energy relaxation on the higher-lying excited states involving the S2 energy levels of carotenoids, including ultrafast carotenoid-to-chlorophyll energy transfer on 90-150 fs timescales.

scholarly journals Energy levels of one-dimensional anharmonic oscillator via neural networks

2019 ◽  
Vol 34 (12) ◽  
pp. 1950088 ◽  
Author(s):  
Halil Mutuk
Keyword(s):  
Neural Network ◽  
Field Theory ◽  
Anharmonic Oscillator ◽  
Energy Levels ◽  
High Accuracy ◽  
Network System ◽  
Quantum Field ◽  
One Dimensional ◽  
Neural Network System ◽  
Good Agreement

In this work, we obtained energy levels of one-dimensional quartic anharmonic oscillator by using neural network system. Quartic anharmonic oscillator is a very important tool in quantum mechanics and also in the quantum field theory. Our results are in good agreement in high accuracy with the reference studies.

scholarly journals The Landau-Zener Transition and the Surface Hopping Method for the 2D Dirac Equation for Graphene

2017 ◽  
Vol 21 (2) ◽  
pp. 313-357 ◽  
Author(s):  
Ali Faraj ◽  
Shi Jin
Keyword(s):  
Dirac Equation ◽  
Electrostatic Potential ◽  
Numerical Experiments ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Two Dimensional ◽  
Lagrangian Surface ◽  
Surface Hopping ◽  
Asymptotic Models ◽  
Semiclassical Regime

AbstractA Lagrangian surface hopping algorithm is implemented to study the two dimensional massless Dirac equation for Graphene with an electrostatic potential, in the semiclassical regime. In this problem, the crossing of the energy levels of the system at Dirac points requires a particular treatment in the algorithm in order to describe the quantum transition—characterized by the Landau-Zener probability— between different energy levels. We first derive the Landau-Zener probability for the underlying problem, then incorporate it into the surface hopping algorithm. We also show that different asymptotic models for this problem derived in [O. Morandi, F. Schurrer, J. Phys. A:Math. Theor. 44 (2011) 265301]may give different transition probabilities. We conduct numerical experiments to compare the solutions to the Dirac equation, the surface hopping algorithm, and the asymptotic models of [O. Morandi, F. Schurrer, J. Phys. A: Math. Theor. 44 (2011) 265301].

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