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The Principles of Quantum Mechanics
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The article was published on 1930-01-01 and is currently open access. It has received 5991 citations till now. The article focuses on the topics: Quantum statistical mechanics & Open quantum system.read more
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Fractional derivatives with no-index law property: Application to chaos and statistics
TL;DR: In this article, the authors showed that fractional operators obeying index law cannot model real world problems taking place in two states, more precisely they cannot describe phenomena taking place beyond their boundaries, as they are scaling invariant, more specifically their results show that, mathematical models based on these differential operators are not able to describe the inverse memory, meaning the full history of a physical problem cannot be described accurately using these derivatives with index law properties.
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A B-spline approach for empirical mode decompositions
TL;DR: An alternative B-spline approach for empirical mode decompositions for nonlinear and nonstationary signals is proposed and recursive formulas of the Hilbert transform of B- Splines are derived and Euler splines as spline intrinsic mode functions in the decomposition are discussed.
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Local formulation and measurements of interfacial area concentration in two-phase flow
TL;DR: In this paper, the local instantaneous formulation of the interfacial area concentration is introduced, and time and spatial averaged area concentrations are derived, and the local ergodic theorem is obtained for stationary developed two-phase flow based on the two-fluid model.
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Quantum mechanics of classically non-integrable systems
TL;DR: In the semiclassical limit, quantum mechanics shows differences between classically integrable abd chaotic systems as discussed by the authors, and a review of recent developments in this field is presented in this paper.
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A Calculation of the Phonon Frequencies in Sodium
TL;DR: In this article, the phonon spectrum of sodium is calculated in the harmonic approximation and the effective interaction between the ions is separated into direct two-body forces between bare ions and effective attraction due to the presence of conduction electrons.