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MathGroup Archive 1999

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difference equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg20567] difference equations
  • From: psalzman at landau.ucdavis.edu
  • Date: Sat, 30 Oct 1999 00:14:12 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

dear all,

i wrote a difference equation at low order, and looked at the same thing at
higher order.  it's absurd.   so it's Mathematica or nothing since i have no grad
students to pawn off the work to (i am a grad student).

here's the basic starting point:

(* a = dt/(2 hbar)  and  b = -hbar^2/(2 m)   *)
(1 + I a * H) Psi[j + 1, i] == (1 - I a * H) Psi[j, i]

i would like 
    H -> b(1/r[i]^2) deriv_r(r[i]^2 deriv_r) + V[j + 1, i] 
on the left, but
    H -> b(1/r[i]^2) deriv_r(r[i]^2 deriv_r) + V[j, i]
on the right.   how can i do this?

also, my 'stubs' for the derivative, deriv_r shouldn't commute with
anything, and Mathematica likes to commute stuff.  is there a way to tell it that
i want deriv_r to remain on the left side of whatever it starts out to the
left of?

lastly, i'm using Psi[j, i], etc  to mean Psi at time j, grid i.   is there
a better way of doing this?

these are some basic questions, i know.  but up until now all i've ever used
Mathematica for is to solve integrals, plot graphs and spacetimes.

thanks!
pete



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