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
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
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.
