A new approach to bound states in potential wells

2001 ◽  
Vol 69 (11) ◽  
pp. 1177-1181 ◽  
Author(s):  
J.-F. Bloch ◽  
V. Ignatovich
Keyword(s):  
Bound States ◽  
Potential Wells ◽  
New Approach

A New Approach to Solution of Time-Independent One-Dimensional Schrödinger Wave Equation

2020 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Wave Equation ◽  
Bound States ◽  
Linear Time ◽  
Potential Well ◽  
Scattering Problems ◽  
Potential Wells ◽  
New Approach ◽  
Transmission Coefficients ◽  
Time Varying Systems ◽  
Arbitrary Potential

Abstract A new approach has been developed in this paper to solve time-independent Schrödinger wave equation for any arbitrary potential and space varying mass as well. The method is based on the state transition matrix used in the analysis of linear time-varying systems, and can determine both bound states and reflection and transmission coefficients associated with scattering problems. Numerical examples for the computation of eigenvalues and eigenmodes associated with bound states are presented for quadratic potential, quartic potential, constant potential well and arbitrary potential well with both constant and space-varying or position-dependent masses. Similarly, transmission coefficients for scattering problems without any infinite potential, and time delays for scattering problems with an infinite potential are computed for arbitrary potential wells.

New Approach to Calculate Adiabatic Curves of Bound States and Reactive Scattering in Quantum Chemistry Problems

2016 ◽  
pp. 455-469
Author(s):  
Fernanda Castelo Branco de Santana ◽  
Angelo Amâncio Duarte ◽  
Mirco Ragni ◽  
Ana Carla Peixoto Bitencourt ◽  
Herman Augusto Lepikson
Keyword(s):  
Quantum Chemistry ◽  
Bound States ◽  
Reactive Scattering ◽  
New Approach

Decay of bound states in oscillating potential wells

2018 ◽  
Vol 97 (5) ◽  
Author(s):  
Steffen Weimann ◽  
Toni Eichelkraut ◽  
Alexander Szameit
Keyword(s):  
Bound States ◽  
Potential Wells ◽  
Oscillating Potential

scholarly journals A study of the bound states for square potential wells with position-dependent mass

2006 ◽  
Vol 360 (2) ◽  
pp. 228-233 ◽  
Author(s):  
A. Ganguly ◽  
Ş. Kuru ◽  
J. Negro ◽  
L.M. Nieto
Keyword(s):  
Bound States ◽  
Potential Wells ◽  
Dependent Mass ◽  
Position Dependent Mass

scholarly journals Geometry symmetry-free and Higher-order Optical Bound States in the Continuum

2021 ◽  
Author(s):  
Qingjia Zhou ◽  
Yangyang Fu ◽  
Lujun Huang ◽  
Qiannan Wu ◽  
Andrey Miroshnichenko ◽  
...  
Keyword(s):  
Significant Role ◽  
Bound States ◽  
Higher Order ◽  
Multiple Objects ◽  
New Approach ◽  
Geometrical Symmetry ◽  
Symmetry Protected ◽  
Zero Index ◽  
The Continuum

Abstract Geometrical symmetry plays a significant role in realizing robust, symmetry-protected, bound states in the continuum (BICs). However, this benefit is only theoretical in many cases since the unavoidable imperfections of fabricated samples may easily break the stringent geometrical requirements. Here we propose an essentially new approach by introducing the concept of geometrical-symmetry-free but symmetry-protected BICs, realized using the static-like environment induced by a zero-index metamaterial (ZIM). We find that robust BICs exist and are protected from the disordered distribution of multiple objects inside ZIM host by its physical symmetries rather than geometrical ones. We further show theoretically and numerically that the existence of those higher-order BICs depends only on the number of objects. By practically designing a structural ZIM waveguide, the existence of BICs is numerically confirmed, as well as their independence on the presence of geometrical symmetry. Our findings provide a new way of realizing higher-order BICs and link their properties to disorder of photonic systems.

The zero-spin glueballs: A new approach to relativistic bound states

1986 ◽  
Vol 31 (2) ◽  
pp. 277-282 ◽  
Author(s):  
G. J. Gounaris ◽  
J. E. Paschalis ◽  
R. K�gerler
Keyword(s):  
Bound States ◽  
New Approach ◽  
Relativistic Bound States

scholarly journals Long-Range Atom–Ion Rydberg Molecule: A Novel Molecular Binding Mechanism

Atoms ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 34
Author(s):  
Markus Deiß ◽  
Shinsuke Haze ◽  
Johannes Hecker Denschlag
Keyword(s):  
Long Range ◽  
Bound States ◽  
Rydberg Atom ◽  
Bound State ◽  
Binding Mechanism ◽  
Potential Wells ◽  
Molecular Binding ◽  
Wave Packet Dynamics ◽  
Rydberg Molecule ◽  
Potential Energy Landscapes

We present a novel binding mechanism where a neutral Rydberg atom and an atomic ion form a molecular bound state at a large internuclear distance. The binding mechanism is based on Stark shifts and level crossings that are induced in the Rydberg atom due to the electric field of the ion. At particular internuclear distances between the Rydberg atom and the ion, potential wells occur that can hold atom–ion molecular bound states. Apart from the binding mechanism, we describe important properties of the long-range atom–ion Rydberg molecule, such as its lifetime and decay paths, its vibrational and rotational structure, and its large dipole moment. Furthermore, we discuss methods of how to produce and detect it. The unusual properties of the long-range atom–ion Rydberg molecule give rise to interesting prospects for studies of wave packet dynamics in engineered potential energy landscapes.

scholarly journals A New Approach to the Non Relativistic Schrödinger Equation for an Energy-Depended Potential V(r,En,l)=V0(1+ηEn,l)r2 in both Noncommutative Three Dimensional Spaces and Phases

2015 ◽  
Vol 60 ◽  
pp. 11-19 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Bound States ◽  
Zeeman Effect ◽  
Three Dimensional ◽  
Energy Spectra ◽  
Noncommutative Space ◽  
New Approach ◽  
3 Dimensional ◽  
New States ◽  
Space Phase ◽  
Ordinary Quantum

In present work we study the 3-dimensional non relativistic and noncommutative space-phase Schrödinger equation for modified potential (see formula in paper) depends on energy and quadratic on the relative distance, we have obtained the exact modified bound-states solutions. It has been observed that, the energy spectra in ordinary quantum mechanics was changed, and replaced by degenerate new states, depending on new discreet quantum numbers:n, l, j and s=±1/2 . We show the noncommutative new anisotropic Hamiltonian containing two new important terms, the first new term describe the spin-orbit interaction while the second describes the modified Zeeman effect.

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