We study the D-dimensional Schr6dinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadraticly on the relative distance. Next, via the Nikiforov-Uvarov （NU） method, we calculate ...We study the D-dimensional Schr6dinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadraticly on the relative distance. Next, via the Nikiforov-Uvarov （NU） method, we calculate the corresponding eigenfunctions and eigenvalues.展开更多
Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric d...Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.展开更多
The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with th...The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunetion is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for D=3, and the resulting energy equation agrees well with that obtained by other methods.展开更多
Approximate analytical solutions of the D-dimensional Klein-Gordon equation are obtained for the scalarand vector general Hulthen-type potential and position-dependent mass with any l by using the concept of supersymm...Approximate analytical solutions of the D-dimensional Klein-Gordon equation are obtained for the scalarand vector general Hulthen-type potential and position-dependent mass with any l by using the concept of supersymmetricquantum mechanics (SUSYQM).The problem is numerically discussed for some cases of parameters.展开更多
Effects of the dimension on the Joule-Thomson expansion are investigated in details by considering the case of d-dimensional(d≥5)charged anti-de Sitter(AdS)black hole which is surrounded by the quintessence with a cl...Effects of the dimension on the Joule-Thomson expansion are investigated in details by considering the case of d-dimensional(d≥5)charged anti-de Sitter(AdS)black hole which is surrounded by the quintessence with a cloud of strings background.Firstly,the thermodynamic quantity of this black hole is reviewed.Secondly,three important features of the Joule-Thomson expansion in different dimensions are discussed,including the Joule-Thomson coefficients,inversion curves,and isenthalpic curves.Finally,the effects of the charge,the quintessence and strings cloud parameters on the Joule-Thomson expansion in the case of six-dimensional black hole are studied.展开更多
In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.
We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstat...We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.展开更多
We present a new approximation scheme for the centrifugal term, and apply this new approach to the SchrSdinger equation with the modified P5schl Teller potential in the -dimension for arbitrary angular momentum state...We present a new approximation scheme for the centrifugal term, and apply this new approach to the SchrSdinger equation with the modified P5schl Teller potential in the -dimension for arbitrary angular momentum states. The approximate analytical solutions of the scattering states are derived. The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the 2 scale and the calculation formula of the phase shifts are given. The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method （APM）.展开更多
We present a new approximation scheme for the centrifugal term,and apply this new approach to the Schrdinger equation with the modified Pschl-Teller potential in the D-dimension for arbitrary angular momentum states.T...We present a new approximation scheme for the centrifugal term,and apply this new approach to the Schrdinger equation with the modified Pschl-Teller potential in the D-dimension for arbitrary angular momentum states.The approximate analytical solutions of the scattering states are derived.The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the k/2π scale and the calculation formula of the phase shifts are given.The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method(APM).展开更多
We consider the D-dimensional SchrSdinger equation under the hyperbolic potential V0（1 -coth（ar））＋ 171 （1 - coth（ar））2. Using a Pekeris-type approximation, the approximate analytical solutions of the problem ...We consider the D-dimensional SchrSdinger equation under the hyperbolic potential V0（1 -coth（ar））＋ 171 （1 - coth（ar））2. Using a Pekeris-type approximation, the approximate analytical solutions of the problem are obtained via the supersymmetric quantum mechanics. The behaviors of energy eigenvalues versus dimension are discussed for various quantum numbers. Useful expectation values as well as the oscillator strength are obtained.展开更多
A scheme for probabilistic remotely preparing N-particle d-dimensional equatorial entangled states via entangled swapping with three parties is presented. The quantum channel is composed of N - 1 pairs of bipartite d-...A scheme for probabilistic remotely preparing N-particle d-dimensional equatorial entangled states via entangled swapping with three parties is presented. The quantum channel is composed of N - 1 pairs of bipartite d-dimensional non-maximally entangled states and a tripartite d-dimension non-maximally entangled state. It is shown that the sender can help either of the two receivers to remotely prepare the original state, and the N-particle projective measurement and the generalized Hadamard transformation are needed in this scheme. The total success probability and classical communication cost are calculated.展开更多
We present analytical bound state solutions of the spin-zero Klein–Gordon （KG） particles in the field of unequal mix-ture of scalar and vector Yukawa potentials within the framework of the approximation scheme to t...We present analytical bound state solutions of the spin-zero Klein–Gordon （KG） particles in the field of unequal mix-ture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov–Uvarov （NU） method. Further, we solve the KG–Yukawa problem for its exact numerical energy eigenvalues via the amplitude phase （AP） method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of the KG–Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 2–6.展开更多
The connection between the number of dimensions and the size of the representation matrices in the Dirac equation has been discussed thoroughly and the restriction N<sup>2</sup> = 2<sup>D</sup>...The connection between the number of dimensions and the size of the representation matrices in the Dirac equation has been discussed thoroughly and the restriction N<sup>2</sup> = 2<sup>D</sup> was derived. In this summary, the result is brought again, this time with emphasis on the importance of irreducibility of the representations. As a counter example, the case of the neutrino is discussed where the above restriction does not hold, indicating that the Dirac equation, in this case, is reducible.展开更多
Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exac...Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.展开更多
The aim of this paper is to prove the a.e.convergence of sequences of the Cesaro and Riesz means of the Walsh–Fourier series of d variable integrable functions.That is,let a=（a1,...,ad）：N→Nd（d∈P）such that aj（...The aim of this paper is to prove the a.e.convergence of sequences of the Cesaro and Riesz means of the Walsh–Fourier series of d variable integrable functions.That is,let a=（a1,...,ad）：N→Nd（d∈P）such that aj（n＋1）≥δsupk≤n aj（k）（j=1,...,d,n∈N）for someδ〉0 and a1（＋∞）=···=ad（＋∞）=＋∞.Then,for each integrable function f∈L1（Id）,we have the a.e.relation for the Cesaro means limn→∞σαa（n）f=f and for the Riesz means limn→∞σα,γa（n）f=f for any 0〈αj≤1≤γj（j=1,...,d）.A straightforward consequence of our result is the so-called cone restricted a.e.convergence of the multidimensional Cesaro and Riesz means of integrable functions,which was proved earlier by Weisz.展开更多
文摘We study the D-dimensional Schr6dinger equation for an energy-dependent Hamiltonian that linearly depends on energy and quadraticly on the relative distance. Next, via the Nikiforov-Uvarov （NU） method, we calculate the corresponding eigenfunctions and eigenvalues.
基金＊Supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2010291, the Professor and Doctor Foundation of Yancheng Teachers University under Grant No. 07YSYJB0203
文摘Using the exponential function transformation approach along with an approximation for the centrifugal potential, the radial Schr6dinger equation of D-dimensional Hulthen potential is transformed to a hypergeometric differential equation. The approximate analytical solutions of scattering states are attained. The normalized wave functions expressed in terms of hypergeometrie functions of scattering states on the ＂k/2π scale＂ and the calculation formula of phase shifts are given. The physical meaning of the approximate analytical solutions is discussed.
基金Supported by the National Natural Science Foundation of China under Grant No 14101020155the Fundamental Research Funds for the Central Universities under Grant No GK201402012
文摘The analytical solutions to the Schrodinger equation with the Eckart potential in arbitrary dimension D is investigated by using the Nikiforov-Uvarov method, and the centrifugal term is treated approximatively with the scheme of Greene and Aldrich. The discrete spectrum is obtained and the wavefunetion is expressed in terms of the Jacobi polynomial or the hypergeometric function. Some special cases of the Eckart potential are discussed for D=3, and the resulting energy equation agrees well with that obtained by other methods.
文摘Approximate analytical solutions of the D-dimensional Klein-Gordon equation are obtained for the scalarand vector general Hulthen-type potential and position-dependent mass with any l by using the concept of supersymmetricquantum mechanics (SUSYQM).The problem is numerically discussed for some cases of parameters.
文摘Effects of the dimension on the Joule-Thomson expansion are investigated in details by considering the case of d-dimensional(d≥5)charged anti-de Sitter(AdS)black hole which is surrounded by the quintessence with a cloud of strings background.Firstly,the thermodynamic quantity of this black hole is reviewed.Secondly,three important features of the Joule-Thomson expansion in different dimensions are discussed,including the Joule-Thomson coefficients,inversion curves,and isenthalpic curves.Finally,the effects of the charge,the quintessence and strings cloud parameters on the Joule-Thomson expansion in the case of six-dimensional black hole are studied.
基金1)This work is supported by NSFC(10571159),SRFDP(2002335090)and KRF(D00008)2)This work is supported by NSFC(10401037)and China Postdoctoral Science Foundation3)This work is supported by the Brain Korea 21 Project in 2005
文摘In this paper, we obtain functional limit theorems for d-dimensional FBM in HSlder norm via estimating large deviation probabilities for d-dimensional FBM in HSlder norm.
基金Project supported by the National Natural Science Foundation of China （Grant No 60261004） and Yunnan Province Science Foundation （Grant No 2002E0008M）.
文摘We construct a general form of propagator in arbitrary dimensions and give an exact wavefunction of a time- dependent forced harmonic oscillator in D（D ≥ 1） dimensions. The coherent states, defined as the eigenstates of annihilation operator, of the D-dimensional harmonic oscillator are derived. These coherent states correspond to the minimum uncertainty states and the relation between them is investigated.
基金Project supported by the Natural Science Foundation of Jiangsu Province, China （Grant No. BK2010291）.
文摘We present a new approximation scheme for the centrifugal term, and apply this new approach to the SchrSdinger equation with the modified P5schl Teller potential in the -dimension for arbitrary angular momentum states. The approximate analytical solutions of the scattering states are derived. The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the 2 scale and the calculation formula of the phase shifts are given. The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method （APM）.
基金Project supported by the Natural Science Foundation of Jiangsu Province,China (Grant No. BK2010291)
文摘We present a new approximation scheme for the centrifugal term,and apply this new approach to the Schrdinger equation with the modified Pschl-Teller potential in the D-dimension for arbitrary angular momentum states.The approximate analytical solutions of the scattering states are derived.The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the k/2π scale and the calculation formula of the phase shifts are given.The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method(APM).
文摘We consider the D-dimensional SchrSdinger equation under the hyperbolic potential V0（1 -coth（ar））＋ 171 （1 - coth（ar））2. Using a Pekeris-type approximation, the approximate analytical solutions of the problem are obtained via the supersymmetric quantum mechanics. The behaviors of energy eigenvalues versus dimension are discussed for various quantum numbers. Useful expectation values as well as the oscillator strength are obtained.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20060357003
文摘A scheme for probabilistic remotely preparing N-particle d-dimensional equatorial entangled states via entangled swapping with three parties is presented. The quantum channel is composed of N - 1 pairs of bipartite d-dimensional non-maximally entangled states and a tripartite d-dimension non-maximally entangled state. It is shown that the sender can help either of the two receivers to remotely prepare the original state, and the N-particle projective measurement and the generalized Hadamard transformation are needed in this scheme. The total success probability and classical communication cost are calculated.
文摘We present analytical bound state solutions of the spin-zero Klein–Gordon （KG） particles in the field of unequal mix-ture of scalar and vector Yukawa potentials within the framework of the approximation scheme to the centrifugal potential term for any arbitrary l-state. The approximate energy eigenvalues and unnormalized wave functions are obtained in closed forms using a simple shortcut of the Nikiforov–Uvarov （NU） method. Further, we solve the KG–Yukawa problem for its exact numerical energy eigenvalues via the amplitude phase （AP） method to test the accuracy of the present solutions found by using the NU method. Our numerical tests using energy calculations demonstrate the existence of inter-dimensional degeneracy amongst the energy states of the KG–Yukawa problem. The dependence of the energy on the dimension D is numerically discussed for spatial dimensions D = 2–6.
文摘The connection between the number of dimensions and the size of the representation matrices in the Dirac equation has been discussed thoroughly and the restriction N<sup>2</sup> = 2<sup>D</sup> was derived. In this summary, the result is brought again, this time with emphasis on the importance of irreducibility of the representations. As a counter example, the case of the neutrino is discussed where the above restriction does not hold, indicating that the Dirac equation, in this case, is reducible.
文摘Deng-Fan potential originally appeared many years ago as an attractive proposition for molecular systems. On the contrary to the ground state of one-dimensional Schr6dinger equation, this potential fails to admit exact analytical solutions for arbitrary quantum number in both relativistic and nonrelativistic regime. Because of this complexity, there exists only few papers, which discuss this interesting problem. Here, using an elegant ansatz, we have calculated the system spectra as well as the eigenfunctions in the general case of unequal vector and scalar potentials under Klein-Gordon equation.
基金Supported by project TMOP-4.2.2.A-11/1/KONV-2012-0051
文摘The aim of this paper is to prove the a.e.convergence of sequences of the Cesaro and Riesz means of the Walsh–Fourier series of d variable integrable functions.That is,let a=（a1,...,ad）：N→Nd（d∈P）such that aj（n＋1）≥δsupk≤n aj（k）（j=1,...,d,n∈N）for someδ〉0 and a1（＋∞）=···=ad（＋∞）=＋∞.Then,for each integrable function f∈L1（Id）,we have the a.e.relation for the Cesaro means limn→∞σαa（n）f=f and for the Riesz means limn→∞σα,γa（n）f=f for any 0〈αj≤1≤γj（j=1,...,d）.A straightforward consequence of our result is the so-called cone restricted a.e.convergence of the multidimensional Cesaro and Riesz means of integrable functions,which was proved earlier by Weisz.
