Re: Quantum Mechanics, Boundary Value Problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg49567] Re: Quantum Mechanics, Boundary Value Problem*From*: Mike <m.HoneychurcNOSPAMh at uq.edu.au>*Date*: Fri, 23 Jul 2004 06:00:48 -0400 (EDT)*Organization*: University of Queensland*References*: <cdnqm4$l7t$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Rob Knapp has written some examples of Schrodinger's equation. Try searching conference proceedings in the information centre. Mike On 22/7/04 5:34 PM, in article cdnqm4$l7t$1 at smc.vnet.net, "anthony danese" <danese at physics.rutgers.edu> wrote: > Hi, > > I'm trying to find a numerical solution to Schrodinger's equation for > a nearly free electron potential (V(x)=Cos(x)) which meets an image > potential which is of the form (V(x)=C - 1/x) where C is a constant. > I can set up the problem using NDSolve, with 2 of my boundary > conditions being continuity of the wave function (psi) and its > derivative(psi') where the 2 potentials meet. The problem is that I > need 2 other boundary conditions--I attempt to arbitrarily set psi = 0 > far into the Cos(x)-like region of the potential and I would like psi > to vanish as for large values of x in the C-1/x region of space. When > I try to run NDSolve, I either get the trivial psi = 0 or I get an > error telling me that the boundary conditions are not well defined. > > As a test, I have tried to run NDSolve to find psi for a step > potential where the step potential is greater than the energy of the > electron. The solution should be free electron-like away from the > step and the solution should decay into the step. This is a problem > that is easily solved analytically but Mathematica doesn't like the > way I'm stating the boundary conditions. Is there anyway to solve > these particular examples of Schrodinger's equation with NDSolve? > > > Any help would be greatly appreciated, > > anthony danese >