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Generalized multiple-mode prolate spheroidal wave functions multi-carrier waveform with index modulation 认领 引用
1
作者 XU Zhichao LU Faping +5 位作者 ZHANG Lifan YANG Dongkai LIU Chuanhui KANG Jiafang AN Qi ZHANG Zhilin 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2025年第2期311-322,共12页
A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The p... A generalized multiple-mode prolate spherical wave functions (PSWFs) multi-carrier with index modulation approach is proposed with the purpose of improving the spectral efficiency of PSWFs multi-carrier systems. The proposed method,based on the optimized multi-index modulation, does not limit the number of signals in the first and second constellations and abandons the concept of limiting the number of signals in different constellations. It successfully increases the spectrum efficiency of the system while expanding the number of modulation symbol combinations and the index dimension of PSWFs signals. The proposed method outperforms the PSWFs multi-carrier index modulation method based on optimized multiple indexes in terms of spectrum efficiency, but at the expense of system computational complexity and bit error performance. For example, with n=10 subcarriers and a bit error rate of 1×10-5,spectral efficiency can be raised by roughly 12.4%. 展开更多
关键词 prolate spherical wave function(PSWF) generalized multiple-mode index modulation spectral efficiency.
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Optimizing basis wave functions in the generator coordinate method for microscopic cluster models (Ⅰ) 认领 引用
2
作者 Yi‑Fan Liu Bo Zhou Yu‑Gang Ma 《Nuclear Science and Techniques》 SCIE EI CAS CSCD 2025年第10期183-191,共9页
We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei 6He and 6Li as examples.By comparing the ground... We employed random distributions and gradient descent methods for the Generator Coordinate Method(GCM)to identify effective basis wave functions,taking halo nuclei 6He and 6Li as examples.By comparing the ground state(0+)energy of 6He and the excited state(0+)energy of 6 Li calculated with various random distributions and manually selected generation coordinates,we found that the heavy tail characteristic of the logistic distribution better describes the features of the halo nuclei.Subsequently,the Adam algorithm from machine learning was applied to optimize the basis wave functions,indicating that a limited number of basis wave functions can approximate the converged values.These results offer some empirical insights for selecting basis wave functions and contribute to the broader application of machine learning methods in predicting effective basis wave functions. 展开更多
关键词 Generator Coordinate Method Effective basis wave functions Nuclear cluster model Machine learning Halo nuclei
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Wave functions of a new kind of nonlinear single-mode squeezed state 认领 引用
3
作者 范洪义 笪诚 陈俊华 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期34-37,共4页
We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）... We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear singlemode squeezing operators. We derive the wave functions of exp[-（ig/2）（（1-X2）1/2P ＋ P（1-X2）1/2）]｜0 in the coordinate representation. A new operator＇s disentangling formula is derived as a by-product. 展开更多
关键词 wave functions nonlinear single-mode squeezed states coordinate representation disentangling formula
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Exact Wave Function of a Time-Dependent Quantum System 认领 引用
4
作者 彭彦泽 彭松清 范天佑 《Journal of Beijing Institute of Technology》 EI CAS 2002年第4期422-423,共2页
To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the... To solve the problem in dispute about a Schrdinger equation with time-depenelent mass and frequency, by means of a simple transformation of variables, the time-dependent Schrdinger equation is transformed into the time-independent one first and then an exact wave function can be found. 展开更多
关键词 quantum system wave function transformation of variables
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Exact Wave Function of a Quantum Oscillator with Time-Dependent Frequency and Driving 认领 引用
5
作者 彭彦泽 彭松清 范天佑 《Journal of Beijing Institute of Technology》 EI CAS 2001年第3期246-249,共4页
The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transf... The harmonic oscillator with time? dependent frequency and driving is studied by means of a new, simple method. By means of simple transformations of variables, the time dependent Schrdinger equation is first transformed into the time independent one. And then exact wave function is found in terms of solutions of the classical equation of motion of the oscillator. 展开更多
关键词 time-dependent harmonic oscillator wave function classical equation of motion
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Wave function collapses and 1/n energy spectrum induced by a Coulomb potential in a one-dimensional flat band system 认领 引用
6
作者 Yi-Cai Zhang 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第5期173-179,共7页
We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential.It is found that,in the presence of a Coulomb potential of type I(with three equal diagonal elements),similarly to ... We investigate the bound state problem in a one-dimensional flat band system with a Coulomb potential.It is found that,in the presence of a Coulomb potential of type I(with three equal diagonal elements),similarly to that in the twodimensional case,the flat band could not survive.At the same time,the flat band states are transformed into localized states with a logarithmic singularity near the center position.In addition,the wave function near the origin would collapse for an arbitrarily weak Coulomb potential.Due to the wave function collapses,the eigen-energies for a shifted Coulomb potential depend sensitively on the cut-off parameter.For a Coulomb potential of type II,there exist infinite bound states that are generated from the flat band.Furthermore,when the bound state energy is very near the flat band,the energy is inversely proportional to the natural number,e.g.,En∝1,n=1,2,3,...It is expected that the 1 energy spectrum could be observed experimentally in the near future. 展开更多
关键词 wave function collapses flat band infinite bound states
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Solution of Dirac Equation with Killingbeck Potential by Using Wave Function Ansatz Method under Spin Symmetry Limit 认领 引用
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作者 M.Hamzavi A.A.Rajabi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第1期35-37,共3页
The Dirac equation is solved for Killingbeck potential. Under spin symmetry limit, the energy eigenvalues and the corresponding wave functions are obtained by using wave function ansatz method.
关键词 Dirac equation Killingbeck potential wave function ansatz method
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Effect of Electron Beam Orientation on Exit Wave Function via Simulation of Electron Dynamic Diffraction 认领 引用
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作者 Yanguo WANG Hongrong LIU +1 位作者 Canying CAI Qibing YANG 《Journal of Materials Science & Technology》 SCIE EI CAS 2007年第5期713-716,共4页
Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result s... Based on the electron dynamic diffraction, phase shift of the exit wave function vs misorientation of the incident electron beam from the exact zone axis has been calculated for the [001] oriented copper. The result shows that the peak of phase shift is the maximum at the atom position as the electron beam along the exact [001] zone axis, and the peak value of phase shift decreases as increases of the misorientation. At small misorientation, i.e. less than 5 degree, change of the phase shift is minimal. The peak value of phase shift decreases significantly when the incident beam deviates form the zone axis over 10 degree and the exit wave has a planar configuration as the misoriention angle arrives -17 degree. The effect of this phase shift characteristics on the information extracted from the hologram has also been considered. 展开更多
关键词 Electron dynamic diffraction Phase shift Exit wave function Misorientation
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FROM WAVE FUNCTIONS TO TAU-FUNCTIONS FOR THE VOLTERRA LATTICE HIERARCHY 认领 引用
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作者 付昂 李明金 杨迪 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期405-419,共15页
For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functio... For an arbitrary solution to the Volterra lattice hierarchy,the logarithmic derivatives of the tau-function of the solution can be computed by the matrix-resolvent method.In this paper,we define a pair of wave functions of the solution and use them to give an expression of the matrix resolvent;based on this we obtain a new formula for the k-point functions for the Volterra lattice hierarchy in terms of wave functions.As an application,we give an explicit formula of k-point functions for the even GUE(Gaussian Unitary Ensemble)correlators. 展开更多
关键词 volterra lattice hierarchy matrix-resolvent method wave functions even GUE correlators
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Double differential cross sections for ionization of H by 75 keV proton impact:Assessing the role of correlated wave functions 认领 引用
10
作者 Jungang Fan Xiangyang Miao Xiangfu Jia 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第12期72-81,共10页
The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum cor... The effect of final-state dynamic correlation is investigated for ionization of atomic hydrogen by 75-keV proton impact by analyzing double differential cross sections.The final state is represented by a continuum correlated wave(CCW-PT)function which accounts for the interaction between the projectile and the target nucleus(PT interaction).The correlated final state is nonseparable solutions of the wave equation combining the dynamics of the electron motion relative to the target and projectile,satisfying the Redmond’s asymptotic conditions corresponding to long range interactions.The transition matrix is evaluated using the CCW-PT function and the undistorted initial state.Both the correlation effects and the PT interaction are analyzed by the present calculations.The convergence of the continuous correlated final state is examined carefully.Our results are compared with the absolute experimental data measured by Laforge et al.[Phys.Rev.Lett.103,053201(2009)]and Schulz et al.[Phys.Rev.A 81,052705(2010)],as well as other theoretical models(especially the results of the latest non perturbation theory).We have shown that the dynamic correlation plays an important role in the ionization of atomic hydrogen by proton impact.While overall agreement between theory and the experimental data is encouraging,detailed agreement is still lacking.However,such an analysis is meaningful because it provides valuable information about the dynamical correlation and PT interaction in the CCW-PT theoretical model. 展开更多
关键词 ionization three-body Coulomb problem correlated wave functions double differential cross section
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A whole-space transform formula of cylindrical wave functions for scattering problems 认领 引用 被引量：2
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作者 Yuan Xiaoming 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2014年第1期23-28,共6页
The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential t... The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems. 展开更多
关键词 scattering transform of wave functions whole-space transform eccentric source multi-sources multi-scatters
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A Direct Calculation of First-Order Wave Function of Helium 认领 引用
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作者 Boniface Otieno Ndinya Joseph Akeyo Omolo 《Communications in Theoretical Physics》 SCIE CAS 2010年第10期647-650,共4页
We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlat... We develop a simple analytic calculation for the first order wave function of helium in a model in which nuclear charge screening is caused by repulsive coulomb interaction. The perturbation term, first-order correlation energy, and first-order wave function are divided into two components, one component associated with the repulsive coulomb interaction and the other proportional to magnetic shielding. The resulting first-order wave functions are applied to calculate second-order energies within the model. We find that the second-order energies are independent of the nuclear charge screening constant in the unperturbed Hamiltonian with a central coulomb potential. 展开更多
关键词 nuclear charge screening first-order wave function and second-order energy
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Scattering of Geometric Algebra Wave Functions and Collapse in Measurements 认领 引用 被引量：4
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作者 Alexander Soiguine 《Journal of Applied Mathematics and Physics》 2020年第9期1838-1844,共7页
The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the ap... The research considers wavelike objects that are elements of even subalgebra of geometric algebra in three dimensions. The used formalism particularly eliminates long existing confusion about the reasons behind the appearance of the imaginary unit in quantum mechanics and introduces clear definition of wave functions. When a wave function acts through the Hopf fibration on a localized geometric algebra element, that is executing a measurement, the result can be named as “collapse” of the wave function. 展开更多
关键词 Wave Functions Geometric Algebra Measurements Scattering Entanglement Dualism
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Calculation of Energy and Other Properties of Muonic Helium Atom Using Boundary Conditions of Wave Function 认领 引用
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作者 B.Rezaei 《Communications in Theoretical Physics》 SCIE CAS 2010年第9期518-520,共3页
The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary ... The properties of muonic helium atom （^4He＋2μ-e-） in ground state are considered. In this work, the energy and average distance between particles have been obtained using a wave function, which satisfies boundary conditions. It is shown that the obtained energy are very close to the values calculated by others. But the small differences of the expectation values of r^2n are due to the incorporated boundary conditions in proposed wave function and are expected. 展开更多
关键词 boundary conditions muonic helium wave function correlation function
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Exact Wave Function and Coherent States for a Time-Dependent Harmonic Oscillator 认领 引用 被引量：1
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作者 PENG Yan-ze PENG Song-qing +1 位作者 FAN Tian-you SUN Ying-fei 《Journal of Beijing Institute of Technology》 EI CAS 2002年第1期101-104,共4页
By using a trial wave function,the exact wave function for a harmonic oscillator with time-dependent mass,frequency,damping and driving is obtained.And then by defining a unitary operator,coherent states for the syste... By using a trial wave function,the exact wave function for a harmonic oscillator with time-dependent mass,frequency,damping and driving is obtained.And then by defining a unitary operator,coherent states for the system of interest are found.These coherent states have most,but not all,of the properties the time independent oscillator.And all the results obtained can be reduced to the usual ones when both the mass and fre-quency are constants and the driving is absent. 展开更多
关键词 harmonic oscillator wave function coherent states
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The Wave Function with Symplectic Symmetry and Its Application 认领 引用 被引量：1
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作者 JIANG Xiao-qin, GUO Jin-liang, LI Ze-sheng, LI Bo-fu and SUN Chia-chung 《Chemical Research in Chinese Universities》 SCIE EI CAS 1993年第1期45-48,共4页
The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The cal... The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination. 展开更多
关键词 Multi-body wave function Symplectic symmetry Correlation energy
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A STUDY OF THE WAVE FUNCTION WITH SYMPLECTIC SYMMETRY^1 认领 引用
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作者 Xiao Qin JIANG Jin Liang GUO Chia Chung SUN 《Chinese Chemical Letters》 SCIE EI CAS 1992年第7期531-532,共2页
By using the linear combination of the AGP(antisymmetrtzed geminat power) and SPG(sequential product of geminats) functions, an attempt has been made to catcutate the ground state of the LiH molecule. The calculated r... By using the linear combination of the AGP(antisymmetrtzed geminat power) and SPG(sequential product of geminats) functions, an attempt has been made to catcutate the ground state of the LiH molecule. The calculated results show that-the AGP or SPG function gives the same ground state result as their linear combination. 展开更多
关键词 AGP A STUDY OF THE WAVE FUNCTION WITH SYMPLECTIC SYMMETRY~1
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Causality of Phase of Wave Function or Can Copenhagen Interpretation of Quantum Mechanics Be Considered Complete? 认领 引用 被引量：1
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作者 Ivan Georgiev Koprinkov 《Journal of Modern Physics》 2016年第4期390-394,共5页
Theoretical and experimental evidences of a causal relation of the phase of the wave function and physical reality are presented. The Copenhagen interpretation of quantum mechanics, which gives physical meaning to the... Theoretical and experimental evidences of a causal relation of the phase of the wave function and physical reality are presented. The Copenhagen interpretation of quantum mechanics, which gives physical meaning to the amplitude of the wave function only, cannot be considered complete on that ground. A new dynamics-statistical interpretation of quantum mechanics is proposed. 展开更多
关键词 Quantum Mechanics Wave Function Material Phase Causality Interpretation
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Explanation of Relation between Wave Function and Probability Density Based on Quantum Mechanics in Phase Space 认领 引用 被引量：1
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作者 Chol Jong Jin-Sim Kim +1 位作者 Shin-Hyok Jon Son-Il Jo 《World Journal of Mechanics》 2023年第1期20-72,共53页
The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamenta... The main problem of quantum mechanics is to elucidate why the probability density is the modulus square of wave function. For the purpose of solving this problem, we explored the possibility of deducing the fundamental equation of quantum mechanics by starting with the probability density. To do so, it is necessary to formulate a new theory of quantum mechanics distinguished from the previous ones. Our investigation shows that it is possible to construct quantum mechanics in phase space as an alternative autonomous formulation and such a possibility enables us to study quantum mechanics by starting with the probability density rather than the wave function. This direction of research is contrary to configuration-space formulation of quantum mechanics starting with the wave function. Our work leads to a full understanding of the wave function as the both mathematically and physically sufficient representation of quantum-mechanical state which supplements information on quantum state given solely by the probability density with phase information on quantum state. The final result of our work is that quantum mechanics in phase space satisfactorily elucidates the relation between the wave function and the probability density by using the consistent procedure starting with the probability density, thus corroborating the ontological interpretation of the wave function and withdrawing a main assumption of quantum mechanics. 展开更多
关键词 Quantum Ensemble Theory Quantum Mechanics In Phase Space Wave Function Probability Density Schrödinger Equation
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Nonlocal Physics in the Wave Function Terminology 认领 引用 被引量：1
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作者 Boris V. Alexeev 《Journal of Applied Mathematics and Physics》 2021年第11期2889-2908,共20页
Shortcomings of the Boltzmann physical kinetics and the Schr&#246;dinger wave mechanics are considered. From the position of nonlocal physics, the Schr&#246;dinger equation is a local equation;this fact leads ... Shortcomings of the Boltzmann physical kinetics and the Schr&#246;dinger wave mechanics are considered. From the position of nonlocal physics, the Schr&#246;dinger equation is a local equation;this fact leads to the great shortcomings of the linear Schr&#246;dinger wave mechanics. Nonlocal nonlinear quantum mechanics is considered using the wave function terminology. 展开更多
关键词 Nonlocal Physics Transport Processes in Quantum Mechanics Shortcomings of the Schrödinger Equation Wave Function Terminology
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