The Experts below are selected from a list of 273 Experts worldwide ranked by ideXlab platform
Barry Simon - One of the best experts on this subject based on the ideXlab platform.
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Tosio Kato’s Work on Non-Relativistic Quantum Mechanics: A Brief Report
Analysis and Operator Theory, 2019Co-Authors: Barry SimonAbstract:We present the highpoints of Tosio Kato’s work on the mathematics behind Non-Relativistic Quantum Mechanics.
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Tosio Kato’s work on non-Relativistic Quantum Mechanics, Part 2
Bulletin of Mathematical Sciences, 2019Co-Authors: Barry SimonAbstract:We review the work of Tosio Kato on the mathematics of non-Relativistic Quantum Mechanics and some of the research that was motivated by this. Topics in this second part include the absence of embedded eigenvalues, trace class scattering, Kato smoothness, the Quantum adiabatic theorem and Kato’s ultimate Trotter Product Formula.
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tosio kato s work on non Relativistic Quantum Mechanics a brief report
2019Co-Authors: Barry SimonAbstract:We present the highpoints of Tosio Kato’s work on the mathematics behind Non-Relativistic Quantum Mechanics.
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Tosio Kato’s work on non-Relativistic Quantum Mechanics: part 1
Bulletin of Mathematical Sciences, 2018Co-Authors: Barry SimonAbstract:We review the work of Tosio Kato on the mathematics of non-Relativistic Quantum Mechanics and some of the research that was motivated by this. Topics in this first part include analytic and asymptotic eigenvalue perturbation theory, Temple–Kato inequality, self-adjointness results, and quadratic forms including monotone convergence theorems.
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Tosio Kato’s work on non-Relativistic Quantum Mechanics, Part 2
Bulletin of Mathematical Sciences, 2018Co-Authors: Barry SimonAbstract:We review the work of Tosio Kato on the mathematics of non-Relativistic Quantum Mechanics and some of the research that was motivated by this. Topics in this second part include absence of embedded eigenvalues, trace class scattering, Kato smoothness, the Quantum adiabatic theorem and Kato’s ultimate Trotter Product Formula.
Yubing Dong - One of the best experts on this subject based on the ideXlab platform.
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PS-meson form factors in Relativistic Quantum Mechanics and constraints from covariant space-time translations
arXiv: Nuclear Theory, 2010Co-Authors: Bertrand Desplanques, Yubing DongAbstract:The role of Poincar\'e covariant space-time translations is investigated in the case of the pseudoscalar-meson charge form factors calculated within a Relativistic Quantum Mechanics framework. It is shown that this role extends beyond the standard energy-momentum conservation, which is accounted for in all works based on this general approach. It implies constraints that have been largely ignored until now but should be nevertheless fulfilled to ensure the full Poincar\'e covariance. The violation of these constraints, which is more or less important depending on the form of Relativistic Quantum Mechanics that is employed, points to the validity of using a single-particle current, which is generally assumed in calculations of form factors. In short, these constraints concern the relation of the momentum transferred to the constituents to the one transferred to the system, which most often differ in Relativistic Quantum Mechanics while they are equal in field theory. How to account for the constraints, as well as restoring the equivalence of different Relativistic Quantum Mechanics approaches in estimating form factors, is discussed. It is mentioned that the result so obtained can be identified to a dispersion-relation one. A short conclusion relative to the underlying dynamics is given in the pion case.
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The E1+/M1+ and S1+/M1+ ratios of γN→Δ(1232) with a point-form Relativistic Quantum Mechanics
Physics Letters B, 2006Co-Authors: Yubing DongAbstract:Abstract The point-form Relativistic Quantum Mechanics is employed to study the photo- and electro-productions of the nucleon resonances. Both the ratios of E 1 + / M 1 + and S 1 + / M 1 + of γ N → Δ transition are calculated. Configuration mixing effect is simply included. The results of the point-form Relativistic Quantum Mechanics indicate that the Relativistic effects provide a remarkable role both on the transition amplitudes and on the two ratios E 1 + / M 1 + and S 1 + / M 1 + . It is found that small deformations of the nucleon and Δ resonance wave functions in D-wave can provides more sizable ratios in the point-form Relativistic Quantum Mechanics than in the conventional non-Relativistic constituent quark model.
Enrique Solano - One of the best experts on this subject based on the ideXlab platform.
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Relativistic Quantum Mechanics with trapped ions
New Journal of Physics, 2011Co-Authors: Lucas Lamata, Jorge Casanova, Rene Gerritsma, Christian F. Roos, Juan José García-ripoll, Enrique SolanoAbstract:We consider the Quantum simulation of Relativistic Quantum Mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the bidimensional Relativistic scattering of single Dirac particles by a linear potential. Furthermore, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena as the confinement and asymptotic freedom of quarks.
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Relativistic Quantum Mechanics with trapped ions
New Journal of Physics, 2011Co-Authors: Lucas Lamata, Jorge Casanova, Rene Gerritsma, Christian F. Roos, Juan Jose Garciaripoll, Enrique SolanoAbstract:We consider the Quantum simulation of Relativistic Quantum Mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. Firstly, we study the bidimensional Relativistic scattering of single Dirac particles by a linear potential. Secondly, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena such as the confinement and asymptotic freedom of quarks.
Alexander J Silenko - One of the best experts on this subject based on the ideXlab platform.
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Position and spin in Relativistic Quantum Mechanics
Physical Review A, 2020Co-Authors: Liping Zou, Pengming Zhang, Alexander J SilenkoAbstract:The problem of the position and spin in Relativistic Quantum Mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are Quantum-mechanical counterparts of the classical position and spin variables. The probabilistic interpretation is valid only for Foldy-Wouthuysen wave functions. The Relativistic spin operators are discussed. The spin-orbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the rest-frame spin are used. Alternative definitions of the orbital angular momentum and the spin are based on noncommutative geometry, do not satisfy standard commutation relations, and can allow the spin-orbit interaction.
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Relativistic Quantum Mechanics of a proca particle in riemannian spacetimes
Physical Review D, 2018Co-Authors: Alexander J SilenkoAbstract:Relativistic Quantum Mechanics of a Proca (spin-1) particle in Riemannian spacetimes is constructed. Covariant equations defining electromagnetic interactions of a Proca particle with the anomalous magnetic moment and the electric dipole moment in Riemannian spacetimes are formulated. The Relativistic Foldy-Wouthuysen transformation with allowance for terms proportional to the zero power of the Planck constant is performed. The Hamiltonian obtained agrees with the corresponding Foldy-Wouthuysen Hamiltonians derived for scalar and Dirac particles and with their classical counterpart. The unification of Relativistic Quantum Mechanics in the Foldy-Wouthuysen representation is discussed.
Lucas Lamata - One of the best experts on this subject based on the ideXlab platform.
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Relativistic Quantum Mechanics with trapped ions
New Journal of Physics, 2011Co-Authors: Lucas Lamata, Jorge Casanova, Rene Gerritsma, Christian F. Roos, Juan José García-ripoll, Enrique SolanoAbstract:We consider the Quantum simulation of Relativistic Quantum Mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. First, we study the bidimensional Relativistic scattering of single Dirac particles by a linear potential. Furthermore, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena as the confinement and asymptotic freedom of quarks.
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Relativistic Quantum Mechanics with trapped ions
New Journal of Physics, 2011Co-Authors: Lucas Lamata, Jorge Casanova, Rene Gerritsma, Christian F. Roos, Juan Jose Garciaripoll, Enrique SolanoAbstract:We consider the Quantum simulation of Relativistic Quantum Mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. Firstly, we study the bidimensional Relativistic scattering of single Dirac particles by a linear potential. Secondly, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena such as the confinement and asymptotic freedom of quarks.
