Re: differential equation with buondary conditions

• To: mathgroup at smc.vnet.net
• Subject: [mg30328] Re: differential equation with buondary conditions
• From: Gustavo Seabra <gseabra at swbell.net>
• Date: Sat, 11 Aug 2001 03:39:50 -0400 (EDT)
• References: <9kqk0f\$4g6\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```I'm sorry. The boundary conditions are, in fact:

1) y[0]==0
2) Int[y[x], x=0, x=a,x]==1 (normalization condition)

The y[a]==0 is used to determine "k". How can I include both boundary
conditions? Also, the answers to this problem are generally given as
"integer multipples of Pi" as n*k*Pi, where n = {0,1,2,...}. Is there a way
to make Mathematica give solutions in this form?

Gustavo.

"Gustavo Seabra" <gseabra at swbell.net> wrote in message
news:9kqk0f\$4g6\$1 at smc.vnet.net...
> 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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