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

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.

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

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

Extrapolation in quantum chemistry: Insights on energetics and reaction dynamics

2020 ◽  
Vol 19 (07) ◽  
pp. 2030001
Author(s):  
A. J. C. Varandas
Keyword(s):  
Quantum Chemistry ◽  
Focal Point ◽  
Reaction Dynamics ◽  
Basis Set ◽  
Reactive Scattering ◽  
Extrapolation Methods ◽  
Computational Quantum Chemistry ◽  
Considerable Impact ◽  
Future Work ◽  
First Time

Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM-[Formula: see text]J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview.

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.

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.

Extending Quantum Chemistry of Bound States to Electronic Resonances

2017 ◽  
Vol 68 (1) ◽  
pp. 525-553 ◽  
Author(s):  
Thomas-C. Jagau ◽  
Ksenia B. Bravaya ◽  
Anna I. Krylov
Keyword(s):  
Quantum Chemistry ◽  
Bound States

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

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