Quantenmechanik

Cohen‐Tannoudji, Claude; Diu, Bernard; Laloë, Franck

doi:10.1515/9783110638769

Cited by 69 publications

(92 citation statements)

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“…(8) can be analyzed in terms of the virial theorem, [47] which for state i is (8) can be analyzed in terms of the virial theorem, [47] which for state i is…”

Section: Electron Distribution At Avoided Crossing Of States and Conimentioning

confidence: 99%

Chemical bonding in excited states: Energy transfer and charge redistribution from a real space perspective

Jara-Cortés¹,

Guevara‐Vela

Pendás

et al. 2017

J Comput Chem

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This work provides a novel interpretation of elementary processes of photophysical relevance from the standpoint of the electron density using simple model reactions. These include excited states of H taken as a prototype for a covalent bond, excimer formation of He to analyze non-covalent interactions, charge transfer by an avoided crossing of electronic states in LiF and conical interesections involved in the intramolecular scrambling in C H . The changes of the atomic and interaction energy components along the potential energy profiles are described by the interacting quantum atoms approach and the quantum theory of atoms in molecules. Additionally, the topological analysis of one- and two-electron density functions is used to explore basic reaction mechanisms involving excited and degenerate states in connection with the virial theorem. This real space approach allows to describe these processes in a unified way, showing its versatility and utility in the study of chemical systems in excited states. © 2017 Wiley Periodicals, Inc.

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“…(8) can be analyzed in terms of the virial theorem, [47] which for state i is (8) can be analyzed in terms of the virial theorem, [47] which for state i is…”

Section: Electron Distribution At Avoided Crossing Of States and Conimentioning

confidence: 99%

Chemical bonding in excited states: Energy transfer and charge redistribution from a real space perspective

Jara-Cortés¹,

Guevara‐Vela

Pendás

et al. 2017

J Comput Chem

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“…At the boundary when r = r c ,

Z = Z_{n_{r}, l}

, and

J_{l} Z_{n_{r}, l} = 0

. Moreover, at r = r c , the energy of a ( n r , l ) state is expressed as

ℰ_{n_{r}, l} = \frac{Z_{n_{r}, l}^{2}}{r_{c}^{2}}

. This

J_{l} ((), Z_{n_{r}, l}) = 0

is a transcendental equation and at a fixed n r , l , this

Z_{n_{r}, l}

is evaluated by the help of MATHEMATICA program package.…”

Section: Resultsmentioning

confidence: 99%

Fisher information in confined isotropic harmonic oscillator

Mukherjee

Roy

2018

Int J of Quantum Chemistry

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Fisher information (I) is investigated in a confined harmonic oscillator (CHO) enclosed in a spherical enclosure, in conjugate r and p spaces. A comparative study between CHO and a free quantum particle in spherical box (PISB), as well as CHO and respective free harmonic oscillator (FHO) is pursued with respect to energy spectrum and I. This reveals that, a CHO offers two exactly solvable limits, namely, a PISB and an FHO. Moreover, the dependence of I on quantum numbers n r, l, m in FHO and CHO are analogous. The role of force constant is discussed. Further, a thorough systematic analysis of I with respect to variation of confinement radius r c is presented, with particular attention on nonzero‐(l, m) states. Considerable new important observations are recorded. The results are quite accurate and most of these are presented for the first time.

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“…Note that real matrices of the form

{boldA}_{ϑ} = (\begin{array}{c} \cos ϑ & - \sin ϑ \\ \sin ϑ & \cos ϑ \end{array}), ϑ \in R,

which describes a rotation in the plane by an angle ϑ , satisfy the condition

\det A_{ϑ} = 1

. Trivially, if ϑ = 0, one obtains the continuity conditions,

{[u (x)]}_{x_{0}} = 0, {[u^{'} (x)]}_{x_{0}} = 0,

at the point x 0 , which are usually imposed in problems of quantum mechanics involving regular potentials . The conditions

{([], u)}_{h_{j}} = {([], u^{'})}_{h_{j}} = 0

( j = 0,1) do not change the domain

H^{2} ((), R)

of the operator

S_{q} = - \frac{d^{2}}{d x^{2}} + q ((), x)

x \in double-struckR

, with

q \in L^{\infty} ((), R)

.…”

Section: Characteristic Equation For a Problem With Two Point Interacmentioning

confidence: 99%

Numerical calculation of the discrete spectra of one‐dimensional Schrödinger operators with point interactions

Barrera-Figueroa

Rabinovich

2018

Math Methods in App Sciences

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In this paper, we consider one‐dimensional Schrödinger operators Sq on double-struckR with a bounded potential q supported on the segment []h0,h1 and a singular potential supported at the ends h0, h1. We consider an extension of the operator Sq in L2()R defined by the Schrödinger operator Hq=−d2dx2+q and matrix point conditions at the ends h0, h1. By using the spectral parameter power series method, we derive the characteristic equation for calculating the discrete spectra of operator Hq. Moreover, we provide closed‐form expressions for the eigenfunctions and associate functions in the Jordan chain given in the form of power series of the spectral parameter. The validity of our approach is proven in several numerical examples including self‐adjoint and nonself‐adjoint problems involving general point interactions described in terms of δ‐ and δ′‐distributions.

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Quantenmechanik

Cited by 69 publications

References 0 publications

Chemical bonding in excited states: Energy transfer and charge redistribution from a real space perspective

Chemical bonding in excited states: Energy transfer and charge redistribution from a real space perspective

Fisher information in confined isotropic harmonic oscillator

Numerical calculation of the discrete spectra of one‐dimensional Schrödinger operators with point interactions

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