In this paper, the Klein-Gordon equation with equal scalar and vector Makaxov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence ...In this paper, the Klein-Gordon equation with equal scalar and vector Makaxov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number l is established and some special cases of Makarov potential axe discussed.展开更多
The Schr(o)dinger equation with the Hulthén potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator.The arbitrary e-wave solutio...The Schr(o)dinger equation with the Hulthén potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator.The arbitrary e-wave solutions are obtained by using an approximation of the centrifugal term.The resulting three-term recursion relation for the expansion coefficients of the wavefunction is presented and the wavefunctions are expressed in terms of the Jocobi polynomial.The discrete spectrum of the bound states is obtained by the diagonalization of the recursion relation.展开更多
In this paper, the Klein-Gordon equation with the spherical symmetric Hulthén potential is turned into a hypergeometric equation and is solved in the framework of function analysis exactly. The corresponding boun...In this paper, the Klein-Gordon equation with the spherical symmetric Hulthén potential is turned into a hypergeometric equation and is solved in the framework of function analysis exactly. The corresponding bound state solutions are expressed in terms of the hypergeometric function, and the energy spectrum of the bound states is obtained as a solution to a given equation by boundary constraints.展开更多
The arbitrary l-wave solutions to the Schrödinger equation for the deformed hyperbolic Eckart potential is investigated analytically by using the Nikiforov–Uvarov method.The centrifugal term is treated with the ...The arbitrary l-wave solutions to the Schrödinger equation for the deformed hyperbolic Eckart potential is investigated analytically by using the Nikiforov–Uvarov method.The centrifugal term is treated with the improved Greene and Aldrich approximation scheme.The wave functions are expressed in terms of the Jacobi polynomial or the hypergeometric function.The discrete spectrum is obtained and it is shown that the deformed hyperbolic Eckart potential is a shape-invariant potential and the bound state energy is independent of the deformation parameter q.展开更多
文摘In this paper, the Klein-Gordon equation with equal scalar and vector Makaxov potentials is studied by the factorization method. The energy equation and the normalized bound state solutions are obtained, a recurrence relation between the different principal quantum number n corresponding to a certain angular quantum number l is established and some special cases of Makarov potential axe discussed.
基金Supported partly by the Scientific Research Foundation of the Education Department of Shaanxi Province under Grant No 2010JK539.
文摘The Schr(o)dinger equation with the Hulthén potential is studied by working in a complete square integrable basis that carries a tridiagonal matrix representation of the wave operator.The arbitrary e-wave solutions are obtained by using an approximation of the centrifugal term.The resulting three-term recursion relation for the expansion coefficients of the wavefunction is presented and the wavefunctions are expressed in terms of the Jocobi polynomial.The discrete spectrum of the bound states is obtained by the diagonalization of the recursion relation.
文摘In this paper, the Klein-Gordon equation with the spherical symmetric Hulthén potential is turned into a hypergeometric equation and is solved in the framework of function analysis exactly. The corresponding bound state solutions are expressed in terms of the hypergeometric function, and the energy spectrum of the bound states is obtained as a solution to a given equation by boundary constraints.
文摘The arbitrary l-wave solutions to the Schrödinger equation for the deformed hyperbolic Eckart potential is investigated analytically by using the Nikiforov–Uvarov method.The centrifugal term is treated with the improved Greene and Aldrich approximation scheme.The wave functions are expressed in terms of the Jacobi polynomial or the hypergeometric function.The discrete spectrum is obtained and it is shown that the deformed hyperbolic Eckart potential is a shape-invariant potential and the bound state energy is independent of the deformation parameter q.
