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MathGroup Archive 2001

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differential equation with buondary conditions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30313] differential equation with buondary conditions
  • From: Gustavo Seabra <gseabra at swbell.net>
  • Date: Wed, 8 Aug 2001 01:34:08 -0400 (EDT)
  • Organization: SBC Internet Services
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

    I'm trying to make Mathematica solve the following:

                            y''[x] + k y[x] == 0

subject to the boundary conditions:
        y[x<0] = 0
        y[x>a] = 0
so that y[x] != 0 only if 0 < x < a.
(yes, it's the "particle in a 1-d box problem.)

If I just do: DSolve[{y''[x] + k y[x]  ==  0}, y[x], x]
it works fine, giving:
{{y[x] -> C[2] Cos[Sqrt[k] x] + C[1] Sin[Sqrt[k] x]}},
which is perfectly ok.

But if I include the boundary conditions y[0] == y[a] == 0,
it doesn't work.

    Any ideas?
--
-----------------------------------------------------------------
Gustavo Seabra - Graduate Student
Chemistry Department
Kansas State University
-----------------------------------------------------------------



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