Simple variational proof that any two‐dimensional potential well supports at least one bound state

1989 ◽  
Vol 57 (1) ◽  
pp. 85-86 ◽  
Author(s):  
K. Yang ◽  
M. de Llano
Keyword(s):  
Bound State ◽  
Two Dimensional ◽  
Potential Well

BOUND STATES AND KLEIN PARADOX OF GRAPHENE SYSTEMS IN CONFINING POTENTIALS

2012 ◽  
Vol 26 (17) ◽  
pp. 1250108
Author(s):  
HAI HUANG ◽  
XIA HUANG
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Bound State ◽  
Linear Potential ◽  
Two Dimensional ◽  
Potential Well ◽  
Klein Paradox ◽  
Confining Potential ◽  
Potential Depth

Two-dimensional massive Dirac equation in both potential well and linear potential is discussed. We find that in the case of potential well, the bound states disappear from the spectrum for large enough potential depth. With the linear confining potential, we show that the Dirac equation presents no bound state. Both these results can be identified as fine examples of the Klein paradox. Applications to graphene systems are also discussed.

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 Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

Bound state in a model of electromagnetic field interacting with a material plan

2020 ◽  
Vol 35 (21) ◽  
pp. 2050170
Author(s):  
Yu. M. Pismak ◽  
D. Shukhobodskaia
Keyword(s):  
Electromagnetic Field ◽  
Maxwell Equations ◽  
Singular Potential ◽  
Bound State ◽  
Material Object ◽  
Two Dimensional ◽  
Isotropic Plane ◽  
Chern Simons ◽  
Material Plane ◽  
State Of Field

In the model with Chern-Simons potential describing the coupling of electromagnetic field with a two-dimensional material, the possibility of the appearance of bound field states, vanishing at sufficiently large distances from interacting with its macro-objects, is considered. As an example of such two-dimensional material object we consider a homogeneous isotropic plane. Its interaction with electromagnetic field is described by a modified Maxwell equation with singular potential. The analysis of their solution shows that the bound state of field cannot arise without external charges and currents. In the model with currents and charges the Chern-Simons potential in the modified Maxwell equations creates bound state in the form of the electromagnetic wave propagating along the material plane with exponentially decreasing amplitude in the orthogonal to its direction.

scholarly journals Fusing N-heteroacene analogues into one “kinked” molecule with slipped two-dimensional ladder-like packing

2016 ◽  
Vol 7 (2) ◽  
pp. 1309-1313 ◽  
Author(s):  
Jing Zhang ◽  
Chengyuan Wang ◽  
Guankui Long ◽  
Naoki Aratani ◽  
Hiroko Yamada ◽  
...  
Keyword(s):  
Charge Transport ◽  
Theoretical Calculations ◽  
Hole Mobility ◽  
Two Dimensional ◽  
Potential Well

An unexpected N-heteroacene with a slipped two-dimensional ladder-like packing feature shows a hole mobility up to 0.3 cm2 V−1 s−1, while theoretical calculations suggest that this compound possesses potential well-balanced ambipolar charge-transport characteristics.

scholarly journals Surface interaction effects to a Klein–Gordon particle embedded in a Woods–Saxon potential well in terms of thermodynamic functions,

2018 ◽  
Vol 96 (7) ◽  
pp. 843-850 ◽  
Author(s):  
B.C. Lütfüoğlu
Keyword(s):  
Thermodynamic Functions ◽  
State Energy ◽  
Gordon Equation ◽  
Surface Effect ◽  
Bound State ◽  
Point Of View ◽  
Potential Well ◽  
Saxon Potential ◽  
Relativistic Regime ◽  
Klein Gordon

Recently, it has been investigated how the thermodynamic functions vary when the surface interactions are taken into account for a nucleon that is confined in a Woods–Saxon potential well, with a non-relativistic point of view. In this manuscript, the same problem is handled with a relativistic point of view. More precisely, the Klein–Gordon equation is solved in the presence of mixed scalar–vector generalized symmetric Woods–Saxon potential energy that is coupled to momentum and mass. Employing the continuity conditions the bound state energy spectra of an arbitrarily parameterized well are derived. It is observed that, when a term representing the surface effect is taken into account, the character of Helmholtz free energy and entropy versus temperature are modified in a similar fashion as this inclusion is done in the non-relativistic regime. Whereas it is found that this inclusion leads to different characters to internal energy and specific heat functions for relativistic and non-relativistic regimes.

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