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How are quantum eigenfunctions of hydrogen atom related to its classical elliptic orbits? 认领 引用
1
作者 Yi-Xuan Yin Tian-Tian Wang Biao Wu 《Chinese Physics B》 SCIE EI CAS CSCD 2026年第5期293-302,共10页
We show that a highly-excited energy eigenfunctionψnlm(r)of hydrogen atom can be approximated as an equal-weight superposition of classical elliptic orbits with energy En and angular momentum L=√l(l+1)h,and z com... We show that a highly-excited energy eigenfunctionψnlm(r)of hydrogen atom can be approximated as an equal-weight superposition of classical elliptic orbits with energy En and angular momentum L=√l(l+1)h,and z component of angular momentum Lz=mh.This correspondence is established by comparing the quantum probability distribution|ψnlm(r)|2and the classical probability distribution pc(r)of an ensemble of such orbits.This finding illustrates a general principle:in the semi-classical limit,an energy eigenstate of a quantum system is in general reduced to a collection of classical orbits,rather than a single classical orbit. 展开更多
关键词 hydrogen energy eigenfunction invariant distribution semiclassical limit
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ERRATUM TO:LOG-CONCAVITY OF THE FIRST DIRICHLET EIGENFUNCTION OF SOME ELLIPTIC DIFFERENTIAL OPERATORS AND CONVEXITY INEQUALITIES FOR THE RELEVANT EIGENVALUE 认领 引用
2
作者 Andrea COLESANTI 《Acta Mathematica Scientia》 SCIE CSCD 2026年第2期1036-1036,共1页
This note contains some corrections to the paper:Colesanti A.Log-concavity of the first Dirichlet eigenfunction of some elliptic differential operators and convexity inequalities for the relevant eigenvalue.Acta Mathe... This note contains some corrections to the paper:Colesanti A.Log-concavity of the first Dirichlet eigenfunction of some elliptic differential operators and convexity inequalities for the relevant eigenvalue.Acta Mathematica Scientia,2025,45B(1):143-152. 展开更多
关键词 log concavity dirichlet eigenfunction elliptic differential operators convexity inequalities
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Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates 认领 引用 被引量：10
3
作者 WANG Hua Alatancang HUANG Jun-Jie 《Communications in Theoretical Physics》 SCIE CAS 2009年第12期1087-1092,共6页
The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonia... The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method. 展开更多
关键词 free vibration of rectangular thin plate double symplectic eigenfunction expansion method upper triangular matrix differential system general solution
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The symplectic eigenfunction expansion theorem and its application to the plate bending equation 认领 引用 被引量：5
4
作者 黄俊杰 阿拉坦仓 王华 《Chinese Physics B》 SCIE EI CAS 2009年第9期3616-3623,共8页
This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite... This paper deals with the bending problem of rectangular plates with two opposite edges simply supported. It is proved that there exists no normed symplectic orthogonal eigenfunction system for the associated infinite-dimensional Hamiltonian operator H and that the two block operators belonging to Hamiltonian operator H possess two normed symplectic orthogonal eigenfunction systems in some space. It is demonstrated by using the properties of the block operators that the above bending problem can be solved by the symplectic eigenfunction expansion theorem, thereby obtaining analytical solutions of rectangular plates with two opposite edges simply supported and the other two edges supported in any manner. 展开更多
关键词 plate bending equation symplectic eigenfunction expansion theorem infinite dimensional Hamiltonian operator analytical solution
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Solving ground eigenvalue and eigenfunction of spheroidal wave equation at low frequency by supersymmetric quantum mechanics method 认领 引用 被引量：6
5
作者 唐文林 田贵花 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第1期121-127,共7页
The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eige... The spheroidal wave functions are found to have extensive applications in many branches of physics and mathematics. We use the perturbation method in supersymmetric quantum mechanics to obtain the analytic ground eigenvalue and the ground eigenfunction of the angular spheroidal wave equation at low frequency in a series form. Using this approach, the numerical determinations of the ground eigenvalue and the ground eigenfunction for small complex frequencies are also obtained. 展开更多
关键词 spheroidal wave equation the perturbation method in supersymmetric quantum mechanics super-potential eigenvalue and eigenfunction
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Symplectic eigenfunction expansion theorem for elasticity of rectangular planes with two simply-supported opposite sides 认领 引用 被引量：5
6
作者 侯国林 阿拉坦仓 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第10期1241-1250,共10页
The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement a... The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region.The completeness of the eigenfunctions is then proved,providing the feasibility of using separation of variables to solve the problems.A general solution is obtained with the symplectic eigenfunction expansion theorem. 展开更多
关键词 plane elasticity problem Hamiltonian system symplectic orthogonality eigenfunction expansion Hamiltonian operator
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Ground eigenvalue and eigenfunction of a spin-weighted spheroidal wave equation in low frequencies 认领 引用 被引量：4
7
作者 唐文林 田贵花 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第5期33-43,共11页
Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their an... Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined. 展开更多
关键词 spin-weighted spheroidal wave equation perturbation method in supersymmetric quantum mechanics super-potential eigenvalue and eigenfunction
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Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation 认领 引用 被引量：1
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作者 黄俊杰 阿拉坦仓 王华 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第8期1039-1048,共10页
This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial diffe... This paper proposes an eigenfunction expansion method to solve twodimensional （2D） elasticity problems based on stress formulation. By introducing appropriate state functions, the fundamental system of partial differential equations of the above 2D problems is rewritten as an upper triangular differential system. For the associated operator matrix, the existence and the completeness of two normed orthogonal eigenfunction systems in some space are obtained, which belong to the two block operators arising in the operator matrix. Moreover, the general solution to the above 2D problem is given by the eigenfunction expansion method. 展开更多
关键词 eigenfunction expansion method two-dimensional （2D） elasticity problem upper triangular differential system general solution
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Squared Eigenfunction Symmetries for the BTL and CTL Hierarchies 认领 引用 被引量：1
9
作者 程纪鹏 贺劲松 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第2期131-136,共6页
In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are expficitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and GTL constraint... In this paper, the squared eigenfunction symmetries for the BTL and CTL hierarchies are expficitly constructed with the suitable modification of the ones for the TL hierarchy, by considering the BTL and GTL constraints. Also the connections with the corresponding additional symmetries are investigated： the squared eigenfunction symmetry generated by the wave function can be viewed as the generating function for the additional symmetries. 展开更多
关键词 squared eigenfunction symmetry the BTL and CTL hierarchies additional symmetries
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A Renormalized-Hamiltonian-Flow Approach to Eigenenergies and Eigenfunctions 认领 引用 被引量：1
10
作者 Wen-Ge Wang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2019年第7期861-868,共8页
We introduce a decimation scheme of constructing renormalized Hamiltonian flows,which is useful in the study of properties of energy eigenfunctions,such as localization,as well as in approximate calculation of eigenen... We introduce a decimation scheme of constructing renormalized Hamiltonian flows,which is useful in the study of properties of energy eigenfunctions,such as localization,as well as in approximate calculation of eigenenergies.The method is based on a generalized Brillouin-Wigner perturbation theory.Each flow is specific for a given energy and,at each step of the flow,a finite subspace of the Hilbert space is decimated in order to obtain a renormalized Hamiltonian for the next step.Eigenenergies of the original Hamiltonian appear as unstable fixed points of renormalized flows.Numerical illustration of the method is given in the Wigner-band random-matrix model. 展开更多
关键词 generalized Brillouin-Wigner perturbation theory Hamiltonian flow eigenfunction structure eigenvalue
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New tomographic reconstruction technique based on Laplacian eigenfunction 认领 引用
11
作者 Yasuhiro SUZUKI Shishir PUROHIT +2 位作者 Satoshi OHDACHI Satoshi YAMAMOTO Kazunobu NAGASAKI 《Plasma Science and Technology》 SCIE EI CAS CSCD 2020年第10期5-9,共5页
This letter proposes a new tomographic reconstruction procedure based on the Laplacian eigenfunction(LEF) patterns, which are independent of the plasma cross-section and do not require the flux surface information. Th... This letter proposes a new tomographic reconstruction procedure based on the Laplacian eigenfunction(LEF) patterns, which are independent of the plasma cross-section and do not require the flux surface information. The process is benchmarked for the experimental data of Heliotron J plasma and the results are compared with the least-squares approximation by a Phillips–Tikhonov(PT)-type regularization, which is widely used as the standard technique for tomographic reconstruction. The reconstruction based on the LEF is found to be capable of determining the magnetic axis at different time locations efficiently in comparison with the PT-type regularization. 展开更多
关键词 tomography Laplacian eigenfunction Heliotron J soft x-ray
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A complete symplectic eigenfunction expansion for the elastic thin plate with simply supported edges 认领 引用
12
作者 Guolin Hou Alatancang Chen 《Theoretical & Applied Mechanics Letters》 EI CAS 2011年第1期10-13,共4页
The eigenvalue problem for the Hamiltonian operator associated with the mathematical model for the deflection of a thin elastic plate is investigated.First,the problem for a rectangular plate with simply supported edg... The eigenvalue problem for the Hamiltonian operator associated with the mathematical model for the deflection of a thin elastic plate is investigated.First,the problem for a rectangular plate with simply supported edges is solved directly.Then,the completeness of the eigenfunctions is proved,thereby demonstrating the feasibility of using separation of variables to solve the problem.Finally,the general solution is obtained by using the proved expansion theorem. 展开更多
关键词 thin plate hamiltonian system symplectic orthogonality eigenfunction expansion hamiltonian operator matrix
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On the Point Spectrum and Non-Degenerate Symplectic Structure of Eigenfunction Systems of Off-Diagonal Infinite Dimensional Hamiltonian Operators 认领 引用
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作者 Jie LIU Jiahui YU Alatancang CHEN 《Journal of Mathematical Research with Applications》 CSCD 2023年第6期710-722,共13页
The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H=(■)are studied in this article.The necessary and sufficient conditions f... The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H=(■)are studied in this article.The necessary and sufficient conditions for the eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H to have non-degenerate symplectic structure are given.Further,the necessary and sufficient conditions for point spectrum to be contained in real axis,imaginary axis and other areas are obtained for off-diagonal infinite dimensional Hamiltonian operator H,respectively.As an illustrating example,off-diagonal infinite dimensional Hamiltonian operators derived from the plate bending problem and string vibration problem are used to justify the conclusions. 展开更多
关键词 point spectrum non-degenerate symplectic structure eigenfunction system off-diagonal infinite dimensional Hamiltonian operator MR(2020)Subject Classification 47A08 47A25 47B02
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A NEW METHOD FOR ESTABLISHING PSEUDO ORTHOGONAL PROPERTIES OF EIGENFUNCTION EXPANSION FORM IN FRACTURE MECHANICS 认领 引用
14
作者 OuZhuocheng ChenYiheng 《Acta Mechanica Solida Sinica》 SCIE 2004年第4期283-289,共7页
A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelect... A new and simple method is developed to establish the pseudo orthogonal properties (POP) of the eigenfunction expansion form (EEF) of crack-tip stress complex potential functions for cracked anisotropic and piezoelectric materials, respectively. Di?erent from previous research, the complex argument separation technique is not required so that cumbersome manipulations are avoided. Moreover, it is shown, di?erent from the previous research too, that the orthogonal properties of the material characteristic matrices A and B are no longer necessary in obtaining the POP of EEF in cracked piezoelectric materials. Of the greatest signi?cance is that the method presented in this paper can be widely extended to treat many kinds of problems concerning path- independent integrals with multi-variables. 展开更多
关键词 eigenfunction expansion form pseudo orthogonal properties Bueckner integral weight function piezoelectric material anisotropic material
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Eigenfunction expansion method of upper triangular operator matrixand application to two-dimensional elasticity problems based onstress formulation 认领 引用
15
作者 额布日力吐 阿拉坦仓 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2012年第2期223-232,共10页
This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem... This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example. 展开更多
关键词 eigenfunction expansion method two-dimensional （2D） elasticity problem,upper triangular operator matrix general solution
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Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity 认领 引用 被引量：3
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作者 齐高娃 侯国林 阿拉坦仓 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第12期264-272,共9页
The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified... The completeness theorem of the eigenfunction systems for the product of two 2 × 2 symmetric operator matrices is proved. The result is applied to 4 × 4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results. 展开更多
关键词 operator matrix Hamiltonian operator symplectic orthogonal eigenfunction system completeness
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Exact Eigenfunctions of N-body System with Quadratic Pair Potential 认领 引用
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作者 王兆亮 王安民 +1 位作者 杨阳 李学超 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第11期639-644,共6页
We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared ... We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave [unctions and the degree of degeneracy. By comparison, we refine A vinash Khare＇s results by making some items in his article precisely. 展开更多
关键词 Calogero-Sutherland model quadratic pair potential exact eigenfunction
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Oscillation Property for the Eigenfunctions of Discrete Clamped Beam Equation and Its Applications 认领 引用
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作者 Yanqiong LU Rui WANG 《Journal of Mathematical Research with Applications》 CSCD 2021年第4期401-415,共15页
In this article,we established the structure of all eigenvalues and the oscillation property of corresponding eigenfunctions for discrete clamped beam equation △4u(k-2)=λm(k)u(k),k∈[2,N+1]Z,u(0)=△u(0)=0=u(N+2)=... In this article,we established the structure of all eigenvalues and the oscillation property of corresponding eigenfunctions for discrete clamped beam equation △4u(k-2)=λm(k)u(k),k∈[2,N+1]Z,u(0)=△u(0)=0=u(N+2)=△u(N+2)with the weight function m:[2,N+1]Z→(0,∞),[2,N+1]Z={2,3,...,N+1}.As an application,we obtain the global structure of nodal solutions of the corresponding nonlinear problems based on the nonlinearity satisfying suitable growth conditions at zero and infinity. 展开更多
关键词 eigenvalue eigenfunctions oscillation property bifurcation point nodal solutions
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Slip flow in an annular sector duct using radial eigenfunctions 认领 引用
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作者 Chang Yi Wang 《Theoretical & Applied Mechanics Letters》 CAS 2014年第3期30-34,共5页
The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow ... The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip. 展开更多
关键词 slip flow radial eigenfunctions annular sector duct
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An l1 Regularized Method for Numerical Differentiation Using Empirical Eigenfunctions 认领 引用
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作者 Junbin LI Renhong WANG Min XU 《Journal of Mathematical Research with Applications》 CSCD 2017年第4期496-504,共9页
We propose an ？~1 regularized method for numerical differentiation using empirical eigenfunctions. Compared with traditional methods for numerical differentiation, the output of our method can be considered directly ... We propose an ？~1 regularized method for numerical differentiation using empirical eigenfunctions. Compared with traditional methods for numerical differentiation, the output of our method can be considered directly as the derivative of the underlying function. Moreover,our method could produce sparse representations with respect to empirical eigenfunctions.Numerical results show that our method is quite effective. 展开更多
关键词 numerical differentiation empirical eigenfunctions ?~1 regularization mercer kernel
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