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 > ----------------------------------------------------------------- > > >