On the number of bound states for the one-dimensional Schrödinger equation
نویسندگان
چکیده
The number of bound states of the one-dimensional Schrödinger equation is analyzed in terms of the number of bound states corresponding to ‘‘fragments’’ of the potential. When the potential is integrable and has a finite first moment, the sharp inequalities 12p1( j51 p N j<N<( j51 p N j are proved, where p is the number of fragments, N is the total number of bound states, and N j is the number of bound states for the j th fragment. When p52 the question of whether N5N1 1N2 or N5N11N221 is investigated in detail. An illustrative example is also provided. © 1998 American Institute of Physics. @S0022-2488~98!03109-0#
منابع مشابه
Numerical solution for one-dimensional independent of time Schrödinger Equation
In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...
متن کاملInvestigation of analytical and numerical solutions for one-dimensional independent-oftime Schrödinger Equation
In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...
متن کاملمعادله بته سالپیتر در فضای ناجابهجایی
We consider Bethe-Salpeter (BS) equation for the bound state of two point particles in the non-commutative space-time. We subsequently explore the BS equation for spin0-spin0, spin1/2-spin1/2 and spin0-spin1/2 bound states. we show that the lowest order spin independent correction to energy spectrum in each case is of the order θ a 4 while the spin dependent one in NC space, is started at the ...
متن کاملApproximate l-state solutions of the D-dimensional Schrödinger equation for Manning-Rosen potential
The Schrödinger equation in D-dimensions for the Manning-Rosen potential with the centrifugal term is solved approximately to obtain bound states eigensolutions (eigenvalues and eigenfunctions). The Nikiforov-Uvarov (NU) method is used in the calculations. We present numerical calculations of energy eigenvalues to twoand four-dimensional systems for arbitrary quantum numbers n and l with three ...
متن کاملBound States of Two-dimensional Schrödinger-newton Equations
We prove an existence and uniqueness result for ground states and for purely angular excitations of two-dimensional Schrödinger-Newton equations. From the minimization problem for ground states we obtain a sharp version of a logarithmic Hardy-Littlewood-Sobolev type inequality.
متن کامل