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Topic: 1D coupling 2nd order ODEs
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heng-chih lin

Posts: 12
Registered: 12/7/04
1D coupling 2nd order ODEs
Posted: Oct 30, 1996 12:20 AM
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[post only Mathematica solutions to this. - moderator]

Hi all,

I am wondering if there exists some programs to calculate the 1D
coupling Schrodinger and Poisson equations like:

_ 2 2
h d
- ----- ---- f (z) - V(z) * f (z) = E (z) (1)
2m 2 i i i
d z

d __ 2
---- V(z) = A(z) + B(z) * \ |f (z)| (2)
2 /_ i
d z i

with boundary conditions:

d V(0) d V(inf)
f (0)= 0; f (inf)=0; ------- = F ; ---------- = G;
i i d z d z

where F and G are known constants.

A(z), B(z) are known functions of z ; fi(z), Ei are i th eigenfunction
and eigenvalue of Schrodinger equation (1). V(z) is a potential function of z.

Thanks in advance for any possible hint, even just solve Schrodinger or Poisson
equation without coupling.


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