Quantum mechanical operator realization of the Stirling numbers theory studied by virtue of the operator Hermite polynomials method

2015 ◽  
Vol 24 (7) ◽  
pp. 070305
Author(s):  
Hong-Yi Fan ◽  
Sen-Yue Lou
Keyword(s):  
Hermite Polynomials ◽  
Stirling Numbers ◽  
Quantum Mechanical ◽  
Operator Realization ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

scholarly journals On the Spectrum of the Local $${\mathbb {P}}^2$$ Mirror Curve

2020 ◽  
Vol 21 (11) ◽  
pp. 3479-3497
Author(s):  
Rinat Kashaev ◽  
Sergey Sergeev
Keyword(s):  
Spectral Problem ◽  
Bethe Ansatz ◽  
Quantum Mechanical ◽  
Planck’S Constant ◽  
Transcendental Equations ◽  
Del Pezzo ◽  
Planck's Constant ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

Abstract We address the spectral problem of the formally normal quantum mechanical operator associated with the quantised mirror curve of the toric (almost) del Pezzo Calabi–Yau threefold called local $${\mathbb {P}}^2$$ P 2 in the case of complex values of Planck’s constant. We show that the problem can be approached in terms of the Bethe ansatz-type highly transcendental equations.

NOISE AND CORRELATED TRANSPORT IN ION CHANNELS

2004 ◽  
Vol 04 (01) ◽  
pp. L171-L178 ◽  
Author(s):  
H. HAKEN
Keyword(s):  
Occupation Number ◽  
Rate Equations ◽  
Quantum Mechanical ◽  
Transition Rates ◽  
Operator Equations ◽  
Occupation Numbers ◽  
Classical Quantum ◽  
The Individual ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

The motion of an ion through a channel is described as a classical/quantum mechanical hopping process between the individual sites of a channel. The transition rates are due to the coupling of an ion to suitable reservoirs. If fluctuating forces are added to the rate equations for the occupation numbers, the equations become quantum mechanical operator equations. Using previous results, the fluctuating forces are uniquely determined by the requirement of quantum mechanical consistency. The resulting equations are solved for several cases and the occupation number fluctuations discussed. Particular emphasis is laid on a model of correlated transport.

NEW n-MODE BOSE OPERATOR REALIZATION OF SU(2) LIE ALGEBRA AND ITS APPLICATION IN ENTANGLED FRACTIONAL FOURIER TRANSFORM

2009 ◽  
Vol 24 (08) ◽  
pp. 615-624 ◽  
Author(s):  
HONG-YI FAN ◽  
SHU-GUANG LIU
Keyword(s):  
Fourier Transform ◽  
Lie Algebra ◽  
Fractional Fourier Transform ◽  
Wave Functions ◽  
Entangled State ◽  
Quantum Mechanical ◽  
Mechanical Wave ◽  
Bose Operator ◽  
Operator Realization ◽  
Multipartite Entangled State

We introduce a new n-mode Bose operator realization of SU(2) Lie algebra and link it to the two mutually conjugate multipartite entangled state representations. In so doing we are naturally lead to the n-mode entangle fractional Fourier transform (EFFT), which provides us with a convenient way to deriving the EFFT of quantum-mechanical wave functions.

DYNAMICAL HAMILTONIAN FOR PREASSIGNED TIME-EVOLUTION OF FERMIONIC SQUEEZING

1999 ◽  
Vol 14 (13) ◽  
pp. 855-862 ◽  
Author(s):  
HONG-YI FAN ◽  
JING-XIAN LIN
Keyword(s):  
Hilbert Space ◽  
Time Evolution ◽  
Orthogonal Transformation ◽  
Quantum Mechanical ◽  
Transformation Matrices ◽  
Operator Realization

We derive the general form of dynamical Hamiltonian generating the preassigned time-evolution of multimode fermionic squeezing. The fermionic squeezing is a quantum-mechanical image in fermionic Hilbert space corresponding to an orthogonal transformation in pseudo-classical Grassmann number space. The derivation is mainly based on the orthogonal properties of the transformation matrices. It is shown that some new fermionic operator realization of SO (2n) group and some new Hamiltonians can be obtained via this approach.

Chemical interpretation: basis set use and the Periodic Table

1992 ◽  
Vol 70 (2) ◽  
pp. 631-635 ◽  
Author(s):  
Leland C. Allen
Keyword(s):  
Periodic Table ◽  
Average Energy ◽  
Binding Energies ◽  
Basis Set ◽  
Strongly Correlated ◽  
Bond Polarity ◽  
Chemical Effects ◽  
And Inversion ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

Examination of contemporary quantum chemistry literature and texts strongly indicates the need for new interpretative measures and indices that have heuristic chemical appeal, but are rigorously defined by physics. A closer look at the Periodic Table in search of such measures leads to configurationenergy (CE), the average energy of a valence electron, which adds a third intrinsic dimension to the Table itself, and is also strongly correlated with atomic energy level spacings. CE can be translated into a quantum mechanical operator whose expectation value in molecules and solids is the Energy Index, EIA. Many chemical effects: rotation and inversion barriers, the anomeric and α-effects, hyperconjugation, etc., appear capable of being quantified, unified, and simplified by EIA, but because it is a one-electron entity, it does not correlate with binding energies or heats of formation. EIA is insitu electronegativity, and systematic release of basis set contraction constraints permits a controlled analysis of bond polarity in terms of radial and angular hybridization changes.

scholarly journals Some Properties of $Q$-Hermite Fubini Numbers and Polynomials

2019 ◽  
Author(s):  
Waseem A. Khan
Keyword(s):  
Generating Functions ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulas

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers.  Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

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