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MathGroup Archive 2004

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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
> 


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