The Experts below are selected from a list of 24 Experts worldwide ranked by ideXlab platform
He Yong-cong - One of the best experts on this subject based on the ideXlab platform.
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Notes on the Bra Vector and Ket Vector, Reciprocal Basis Vectors and Reciprocal Vectors, Covariant Vectors and Contravariant Vectors
Journal of Neijiang Teachers College, 2003Co-Authors: He Yong-congAbstract:The Bra Vector,Ket Vector and metric tensor are introduced directly from the inner produce of two rectors A.B=(A,B) = (A\B); reciprocal basis Vectors and reciprocal Vectors are introduced from representation of a Vector A = AKet = (A .e)ek in affine coordinate system; and the covariant Vector and contrava riavant Vector are introduced from a general orthogonal transformation from one affine coordinate system to another; thus it can seen, these Vectors have been conjugated close, these Vectors are reciprocal to each other and dual to each other.
Md. Abdul Khan - One of the best experts on this subject based on the ideXlab platform.
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Hyperspherical three-body calculation for muonic atoms
'Springer Science and Business Media LLC', 2012Co-Authors: Md. Abdul KhanAbstract:Ground state energies of exotic three-body atomic systems consisting two muons and a positively charged nucleus like: 1H+ μ- μ-, 4He2+ μ− μ−, 3He2+ μ− μ−, 7Li3+ μ− μ−, 6Li3+ μ− μ−, 9Be4+ μ− μ−, 12C6+ μ- μ-, 16O8+ μ- μ-, 20Ne10+ μ−μ−, 28Si14+ μ− μ− and 40Ar18+ μ−μ− have been calculated using hyperspherical harmonics expansion (HHE) method. Calculation of matrix elements of two body interactions involved in the HHE method for a three body system is greatly simplified by expanding the bra- and Ket- Vector states in the hyperspherical harmonics basis states appropriate for the partition corresponding to the interacting pair. This involves the Raynal-Revai coefficients (RRC), which are the transformation coefficients between the hyperspherical harmonics bases corresponding to the two partitions. Use of these coefficients found to be very useful for the numerical solution of three-body Schrödinger equation where the two-body potentials are other than Coulomb or harmonic oscillator type. However, in this work the interaction potentials involved are purely Coulomb. The calculated energies have been compared with (i) those obtained by straight forward manner; and (ii) with those found in the literature (wherever available). The calculated binding energies agree within the computational error
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COMPUTATION OF RAYNAL-REVAI COEFFICIENTS FOR THE HYPERSPHERICAL APPROACH TO A THREE-BODY SYSTEM
2000Co-Authors: Md. Abdul Khan, Sagar K. Dutta, Tapan Kumar DasAbstract:The calculation of matrix elements of two-body interactions needed in the hyper-spherical harmonics method for a three-body system is greatly simplied by ex-panding the bra- and Ket-Vector states in the hyperspherical harmonics basis states appropriate for the partition corresponding to the interacting pair. This involves the Raynal-Revai coecients (RRC) which are the transformation coecients be-tween the hyperspherical harmonics bases corresponding to the two partitions. In this work, we present a fast algorithm for an accurate numerical computation of RRC. We have used this technique for two-electron atoms where the two-body in-teractons are purely Coulombic, and compared the results with the direct numerical integrations. Both the individual matrix element of the total interaction potential as well as the calculated binding energy agree within the computational error
M. Ashrafi - One of the best experts on this subject based on the ideXlab platform.
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A driven damped harmonic oscillator in the Ket-Vector representation of the density operator
Journal of Russian Laser Research, 2013Co-Authors: Mohammad Reza Bazrafkan, M. AshrafiAbstract:By virtue of the entangled-state basis and the Ket-Vector representation of the density operator, we solve the master equation of a driven damped harmonic oscillator. In this representation, the density operators are mapped to Vectors of a two-mode Fock space whose first mode is the system mode and the second mode is a fictitious one. We derive the Glauber–Sudarshan P function of the quantum state.
Kim Keun-young - One of the best experts on this subject based on the ideXlab platform.
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More on complexity of operators in quantum field theory
'Springer Science and Business Media LLC', 2019Co-Authors: Yang Run-qiu, An Yu-sen, Niu Chao, Zhang Cheng-yong, Kim Keun-youngAbstract:Recently it has been shown that the complexity of SU($n$) operator is determined by the geodesic length in a bi-invariant Finsler geometry, which is constrained by some symmetries of quantum field theory. It is based on three axioms and one assumption regarding the complexity in continuous systems. By relaxing one axiom and an assumption, we find that the complexity formula is naturally generalized to the Schatten $p$-norm type. We also clarify the relation between our complexity and other works. First, we show that our results in a bi-invariant geometry are consistent with the ones in a right-invariant geometry such as $k$-local geometry. Here, a careful analysis of the sectional curvature is crucial. Second, we show that our complexity can concretely realize the conjectured pattern of the time-evolution of the complexity: the linear growth up to saturation time. The saturation time can be estimated by the relation between the topology and curvature of SU($n$) groups.Comment: Modified the Sec. 4.1, where we offered a powerful proof: if (1) the Ket Vector and bra Vector in quantum mechanics contain same physics, or (2) adding divergent terms to a Lagrangian will not change underlying physics, then complexity in quantum mechanics must be bi-invariant
Tapan Kumar Das - One of the best experts on this subject based on the ideXlab platform.
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COMPUTATION OF RAYNAL-REVAI COEFFICIENTS FOR THE HYPERSPHERICAL APPROACH TO A THREE-BODY SYSTEM
2000Co-Authors: Md. Abdul Khan, Sagar K. Dutta, Tapan Kumar DasAbstract:The calculation of matrix elements of two-body interactions needed in the hyper-spherical harmonics method for a three-body system is greatly simplied by ex-panding the bra- and Ket-Vector states in the hyperspherical harmonics basis states appropriate for the partition corresponding to the interacting pair. This involves the Raynal-Revai coecients (RRC) which are the transformation coecients be-tween the hyperspherical harmonics bases corresponding to the two partitions. In this work, we present a fast algorithm for an accurate numerical computation of RRC. We have used this technique for two-electron atoms where the two-body in-teractons are purely Coulombic, and compared the results with the direct numerical integrations. Both the individual matrix element of the total interaction potential as well as the calculated binding energy agree within the computational error
