Results 231 to 240 of about 5,169 (253)

Bessel Equation as an Operator Identity's Matrix Element in Quantum Mechanics

Physics Letters, Section A: General, Atomic and Solid State Physics, 2004
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Hong-Yi Fan
exaly   +2 more sources

Approximate Nonsymmetric Solutions of Many-Particle Equations and Some Identities for the Density Matrix

Mathematical Notes, 1996
1. I. I. vorovich, in: Proceedings of H All-Union Congress on Theoretical and Applied Mechanics [in Russian], Vol. 3, Nauka, Moscow (1966), pp. 116-136. 2. V. E. KovaVchuk and I. I. Vorovich, Prikl. Mat. Mekh. [J. Appl. Math. Mech.], 31, No. 5, 861-869 (1967). 3. V. E. Koval~chuk, PriM. Mat. Mekh. [J. Appl. Math. Mech.], as, No. 3, 511-518 (1969).
Victor Maslov, O Yu Shvedov
exaly   +3 more sources

On Systems of Integro-Differential and Integral Equations with Identically Singular Matrix Multiplying the Principal Part

Differential Equations, 2022
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Bulatov, M. V., Solovarova, L. S.
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The number of solutions to the alternate matrix equation over a finite field and a q-identity

Journal of Statistical Planning and Inference, 2001
Let \(F_q\) be a finite field with \(q\) elements, where \(q\) is a power of a prime. In this paper, the authors first correct a counting error for the formula \(N(K_{2\nu}, O^{(m)})\) occurring in a paper by \textit{L. Carlitz} [Arch. Math. 5, 19-31 (1954; Zbl 0056.01702)].
Wei, Hongzeng, Zhang, Yibin
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Equation for Density Matrix Systems of Identical Particles

2020
The equations for the statistical operator and the density matrix are considered here for a single particle and a system of identical particles when dissipative forces act on them. From the equation for the density matrix, a kinetic equation can be obtained when the density matrix is diagonal. These equations are the basis for the study of the simplest
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Equations of motion with the identity mass matrix for holonomic systems

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2004
Some consequences concerning holonomic systems described in terms of the inertial quasi-velocities (IQV) are discussed in this note. Introducing the IQV vector into Lagrange's formulation leads to first-order equations with the identity mass matrix of the system.
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One-dimensional integral equations for a system of three identical particles in the boundary condition model and the possibility of changing the off-shell behaviour of the two-particle T-matrix

Nuclear Physics A, 1976
Abstract It is shown that in the framework of the boundary condition model (BCM) for the two-particle interaction the Schrodinger equation for the system of three identical bosons can be reduced to the one-dimensional integral equation in an exact way.
V.N. Efimov, H. Schulz
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(w; β)-BELL POLYNOMIALS ∀w ∈ C, β > 0, THEIR APPLICATIONS IN IDENTITIES EVALUATION AND MATRIX EQUATION REPRESENTATION

jnanabha
In the present paper on application of (w; β)-Bell polynomials ∀w ∈ C, β > 0, authors obtain identities of Kummer confluent hypergeometric function and Srivastava - Daoust function of two variables. Next they derive that the differentiation of these polynomials is connected with Stirling numbers of second kind.
R. C. Singh Chandel, Hemant Kumar, null J. L´opez-Bonilla   +2 more
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Canonical Equation K 32 for Normalized Spectral Functions of Random Gram Matrices with Identically Distributed Independent Blocks. Block Matrix Density

2001
The Chapter extends the “One quarter Law” \( {(2\pi )^{ - 1}}\sqrt {(4 - x)} \;{x^{ - 1/2}},\;{\rm{0}}\;{\rm{ < }}\;x {\rm{ < }}\;{\rm{4}} \) to Gram random matrices with independent random blocks obeying a Lindeberg-type condition and allowing arbitrary dependence of entries within each block.
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Canonical Equation K 28 for Normalized Spectral Functions of Random Symmetric Matrices with Identically Distributed Independent Blocks. Block Matrix Density. SS-Laws

2001
The first asymptotics of normalized spectral functions of random matrices were obtained for the matrices with independent entries. As we have seen in the previous chapter, it is possible to find the general form of possible limit normalized spectral functions of random symmetric matrices with asymptotically independent random blocks.
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