We all physicist have long been believed that an elementary particle is a wave as well as a particle, but we discuss in this paper that an electron (probably all fermions) is always a particle. Author claim that quant...We all physicist have long been believed that an elementary particle is a wave as well as a particle, but we discuss in this paper that an electron (probably all fermions) is always a particle. Author claim that quantum mechanics (QM) is not such mysterious as Bohr stated that the wave turn to the particle by observation. We can understand QM by natural human sense. The wave nature of electrons is only an appearance or a phenomena but not intrinsic or substantial. An electron is an individual body, which interferes with other individual electrons. Interference is the key word instead of the wave to understand the quantum mechanics. Interference produces the wave nature and the uncertainty. When we determine that an electron is nothing but a particle, we will see the true meaning of wave function and the Schr?dinger’s equation.展开更多
In this paper, the one-dimensional time dependent Schr?dinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evo...In this paper, the one-dimensional time dependent Schr?dinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff Ordinary Differential Equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10?4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.展开更多
The paper applies a one-to-one correspondence which exists between individual Schr?dinger perturbation terms and the diagrams obtained on a circular scale of time to whole sets of the Schr?dinger terms belonging to a ...The paper applies a one-to-one correspondence which exists between individual Schr?dinger perturbation terms and the diagrams obtained on a circular scale of time to whole sets of the Schr?dinger terms belonging to a definite perturbation order. In effect the diagram properties allowed us to derive the recurrence formulae giving the number of higher perturbative terms from the number of lower order terms. This recurrence formalism is based on a complementary property that any perturbation order N can be composed of two positive integer components Na , Nb combined into N in all possible ways. Another result concerns the degeneracy of the perturbative terms. This degeneracy is shown to be only twofold and the terms having it are easily detectable on the basis of a circular scale. An analysis of this type demonstrates that the degeneracy of the perturbative terms does not exist for very low perturbative orders. But when the perturbative order exceeds five, the number of degenerate terms predominates heavily over that of nondegenerate terms.展开更多
In this paper, we coupled the Quantum Mechanics conventional Schrödinger’s equation, for the particles, with the Maxwell’s wave equation, in order to study the potential’s role on the conversion of the ele...In this paper, we coupled the Quantum Mechanics conventional Schrödinger’s equation, for the particles, with the Maxwell’s wave equation, in order to study the potential’s role on the conversion of the electromagnetic field energy to mass and vice versa. We show that the dissipation (“conductivity”) factor and the particle implicit proper frequency are both related to the potential energy. We have also derived a new expression for the Schrödinger’s Equation considering the potential energy into this equation not as an ad hoc term, but also as an operator (Hermitian), which has the scalar potential energy as a natural eigenvalue of this operator.展开更多
We point out that a suitable scale of time for the Schrödinger perturbation process is a closed line having rather a circular and not a conventional straight-linear character. A circular nature of the scale c...We point out that a suitable scale of time for the Schrödinger perturbation process is a closed line having rather a circular and not a conventional straight-linear character. A circular nature of the scale concerns especially the time associated with a particular order N of the perturbation energy which provides us with a full number of the perturbation terms predicted by Huby and Tong. On the other hand, a change of the order N—connected with an increased number of the special time points considered on the scale—requires a progressive character of time. A classification of the perturbation terms is done with the aid of the time-point contractions present on a scale characteristic for each N. This selection of terms can be simplified by a partition procedure of the integer numbers representing N-1. The detailed calculations are performed for the perturbation energy of orders N=7 and N=8 .展开更多
Recently we proposed “a new interpretation of quantum mechanics (called quantum and classical measurement theory)” in this journal (JQIS: Vol. 1, No. 2), which was characterized as the metaphysical and linguistic tu...Recently we proposed “a new interpretation of quantum mechanics (called quantum and classical measurement theory)” in this journal (JQIS: Vol. 1, No. 2), which was characterized as the metaphysical and linguistic turn of quantum mechanics. This turn from physics to language does not only realize the remarkable extension of quantum mechanics but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics). And thus, the turn urges us to dream that traditional philosophies (i.e., Parmenides, Plato, Aristotle, Descartes, John Locke, Berkeley, Hume, Kant, Saussure, Wittgenstein, etc.) can be understood in the quantum mechanical world view. This dream will be challenged in this paper. We, of course, know that most scientists are skeptical to philosophy. Still, we can expect that readers find a good linguistic philosophy (i.e. philosophy of language) in quantum mechanics.展开更多
Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. ...Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. Quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schr?dinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.展开更多
In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We ...In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We also describe the loss of smoothness of classical solutions for the Navier-Stokes equations.展开更多
A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in t...A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.展开更多
The paper demonstrates deep unity of classic and quantum physics at the space thermostat (ST) presence, which fulfilled all space by the temperature T0 = 2.73 K. The ST presents itself the Cosmic Microwave Background ...The paper demonstrates deep unity of classic and quantum physics at the space thermostat (ST) presence, which fulfilled all space by the temperature T0 = 2.73 K. The ST presents itself the Cosmic Microwave Background (CMB). From the main quantum position we consider the ST/CMB as the wave function carrier (“quantum background”). The paper is devoted to ST/CMB medium the classic conservation laws of mass, momentum and energy. We show the soliton like solutions of our classic model correspond to Schrodinger’s quantum solutions, demonstrate the atom hydrogen specter and other quantum peculiarities. The paper contains typical technical examples classic/ quantum simulation at the ST presence.展开更多
The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Nav...The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided.展开更多
This study successfully reveals the dark,singular solitons,periodic wave and singular periodic wave solutions of the(1+1)-dimensional coupled nonlinear Schr?dinger equation by using the extended rational sine-cosine a...This study successfully reveals the dark,singular solitons,periodic wave and singular periodic wave solutions of the(1+1)-dimensional coupled nonlinear Schr?dinger equation by using the extended rational sine-cosine and rational sinh-cosh methods.The modulation instability analysis of the governing model is presented.By using the suitable values of the parameters involved,the 2-,3-dimensional and the contour graphs of some of the reported solutions are plotted.展开更多
The purpose of this paper is to verify that the computational scheme from[Heid et al.,Gradient flow finite element discretizations with energy-based adaptivity for the Gross–Pitaevskii equation,J.Comput.Phys.436(2021...The purpose of this paper is to verify that the computational scheme from[Heid et al.,Gradient flow finite element discretizations with energy-based adaptivity for the Gross–Pitaevskii equation,J.Comput.Phys.436(2021)]for the numerical approximation of the ground state of the Gross–Pitaevskii equation can equally be applied for the effective approximation of excited states of Schr¨odinger’s equation.That procedure employs an adaptive interplay of a Sobolev gradient flow iteration and a novel local mesh refinement strategy,and yields a guaranteed energy decay in each step of the algorithm.The computational tests in the present work highlight that this strategy is indeed able to approximate excited states,with(almost)optimal convergence rate with respect to the number of degrees of freedom.展开更多
文摘We all physicist have long been believed that an elementary particle is a wave as well as a particle, but we discuss in this paper that an electron (probably all fermions) is always a particle. Author claim that quantum mechanics (QM) is not such mysterious as Bohr stated that the wave turn to the particle by observation. We can understand QM by natural human sense. The wave nature of electrons is only an appearance or a phenomena but not intrinsic or substantial. An electron is an individual body, which interferes with other individual electrons. Interference is the key word instead of the wave to understand the quantum mechanics. Interference produces the wave nature and the uncertainty. When we determine that an electron is nothing but a particle, we will see the true meaning of wave function and the Schr?dinger’s equation.
基金Ministry of Education and Science of the Republic of Kazakhstan for a grant,and the“Factor”Company of System Researches for combining our efforts in this projectpart of the international project“Joint Kazakh-Indian study the influence of anthropogenic factors on atmospheric phenomena on the basis of numerical weather prediction models WRF(Weather Research and Forecasting)”,commissioned by the Ministry of Education and Science of the Republic of Kazakhstan.
文摘The analytic properties of the scattering amplitude are discussed. And, the representation of the potential by the scattering amplitude is obtained.
文摘In this paper, the one-dimensional time dependent Schr?dinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff Ordinary Differential Equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10?4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.
文摘The paper applies a one-to-one correspondence which exists between individual Schr?dinger perturbation terms and the diagrams obtained on a circular scale of time to whole sets of the Schr?dinger terms belonging to a definite perturbation order. In effect the diagram properties allowed us to derive the recurrence formulae giving the number of higher perturbative terms from the number of lower order terms. This recurrence formalism is based on a complementary property that any perturbation order N can be composed of two positive integer components Na , Nb combined into N in all possible ways. Another result concerns the degeneracy of the perturbative terms. This degeneracy is shown to be only twofold and the terms having it are easily detectable on the basis of a circular scale. An analysis of this type demonstrates that the degeneracy of the perturbative terms does not exist for very low perturbative orders. But when the perturbative order exceeds five, the number of degenerate terms predominates heavily over that of nondegenerate terms.
文摘In this paper, we coupled the Quantum Mechanics conventional Schrödinger’s equation, for the particles, with the Maxwell’s wave equation, in order to study the potential’s role on the conversion of the electromagnetic field energy to mass and vice versa. We show that the dissipation (“conductivity”) factor and the particle implicit proper frequency are both related to the potential energy. We have also derived a new expression for the Schrödinger’s Equation considering the potential energy into this equation not as an ad hoc term, but also as an operator (Hermitian), which has the scalar potential energy as a natural eigenvalue of this operator.
文摘We point out that a suitable scale of time for the Schrödinger perturbation process is a closed line having rather a circular and not a conventional straight-linear character. A circular nature of the scale concerns especially the time associated with a particular order N of the perturbation energy which provides us with a full number of the perturbation terms predicted by Huby and Tong. On the other hand, a change of the order N—connected with an increased number of the special time points considered on the scale—requires a progressive character of time. A classification of the perturbation terms is done with the aid of the time-point contractions present on a scale characteristic for each N. This selection of terms can be simplified by a partition procedure of the integer numbers representing N-1. The detailed calculations are performed for the perturbation energy of orders N=7 and N=8 .
文摘Recently we proposed “a new interpretation of quantum mechanics (called quantum and classical measurement theory)” in this journal (JQIS: Vol. 1, No. 2), which was characterized as the metaphysical and linguistic turn of quantum mechanics. This turn from physics to language does not only realize the remarkable extension of quantum mechanics but also yield the quantum mechanical world view (i.e., the philosophy of quantum mechanics). And thus, the turn urges us to dream that traditional philosophies (i.e., Parmenides, Plato, Aristotle, Descartes, John Locke, Berkeley, Hume, Kant, Saussure, Wittgenstein, etc.) can be understood in the quantum mechanical world view. This dream will be challenged in this paper. We, of course, know that most scientists are skeptical to philosophy. Still, we can expect that readers find a good linguistic philosophy (i.e. philosophy of language) in quantum mechanics.
文摘Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. Quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schr?dinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.
基金the Ministry of Education and Science of the Republic of Kazakhstan for a grant
文摘In this work, we present final solving Millennium Prize Problems formulated by Clay Math. Inst., Cambridge. A new uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided. We also describe the loss of smoothness of classical solutions for the Navier-Stokes equations.
文摘A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.
文摘The paper demonstrates deep unity of classic and quantum physics at the space thermostat (ST) presence, which fulfilled all space by the temperature T0 = 2.73 K. The ST presents itself the Cosmic Microwave Background (CMB). From the main quantum position we consider the ST/CMB as the wave function carrier (“quantum background”). The paper is devoted to ST/CMB medium the classic conservation laws of mass, momentum and energy. We show the soliton like solutions of our classic model correspond to Schrodinger’s quantum solutions, demonstrate the atom hydrogen specter and other quantum peculiarities. The paper contains typical technical examples classic/ quantum simulation at the ST presence.
基金the Ministry of Education and Science of the Republic of Kazakhstan for a grant,and to the System Research“Factor”Company for combining our efforts in this projectpart of an international project,“Joint Kazakh-Indian studies of the influence of anthropogenic factors on atmospheric phenomena on the basis of numerical weather prediction models WRF(Weather Research and Forecasting)”,commissioned by the Ministry of Education and Science of the Republic of Kazakhstan.
文摘The analytic properties of the scattering amplitude are discussed, and a representation of the potential is obtained using the scattering amplitude. A uniform time estimation of the Cauchy problem solution for the Navier-Stokes equations is provided.
文摘This study successfully reveals the dark,singular solitons,periodic wave and singular periodic wave solutions of the(1+1)-dimensional coupled nonlinear Schr?dinger equation by using the extended rational sine-cosine and rational sinh-cosh methods.The modulation instability analysis of the governing model is presented.By using the suitable values of the parameters involved,the 2-,3-dimensional and the contour graphs of some of the reported solutions are plotted.
基金the financial support of the Swiss National Science Foundation(SNSF),Project No.P2BEP2_191760.
文摘The purpose of this paper is to verify that the computational scheme from[Heid et al.,Gradient flow finite element discretizations with energy-based adaptivity for the Gross–Pitaevskii equation,J.Comput.Phys.436(2021)]for the numerical approximation of the ground state of the Gross–Pitaevskii equation can equally be applied for the effective approximation of excited states of Schr¨odinger’s equation.That procedure employs an adaptive interplay of a Sobolev gradient flow iteration and a novel local mesh refinement strategy,and yields a guaranteed energy decay in each step of the algorithm.The computational tests in the present work highlight that this strategy is indeed able to approximate excited states,with(almost)optimal convergence rate with respect to the number of degrees of freedom.
