Need help to a beginner.
- To: mathgroup at smc.vnet.net
- Subject: [mg9642] Need help to a beginner.
- From: shink at iastate.edu (Shinichiro Kondo)
- Date: Mon, 17 Nov 1997 19:49:51 -0500
- Organization: Iowa State University, Ames, Iowa (USA)
- Sender: owner-wri-mathgroup at wolfram.com
Hi, all. I am quite new to Mathematica, and am using the older version, v. 2.2. I hope someone will help me. My problem is nothing to do with homework of a math class, or any sort. I am a physics graduate student, and for my research project am trying to have an algebraic expression of potential energy of certain ionic crystalline lattice. The electrostatic (i.e. Coulomb) energy has the expression of 1/r, where r is the distance between two charges. I am still far from getting the answer I want because of this problem I am facing in the very first stage where I am supposed to be used to Mathematica. First of all, let me explain my problem. It is known, if you expand 1/Sqrt[1-x], provided that x^2<<1, you have 1+(1/2)*x+(3/*)*x^2+(5/16)*x^3+.... Now, let's have a similar expression to this: 1/Sqrt[(a-x)^2+y^2+z^2]. Suppose x, y and z are cartesian coordinates, and r^2=x^2+y^2+z^2. And a is some positive constant, and it satisfies a>>r. So factoring the denominator by a^2 and kicking it out of the Sqrt as a, I can continue this algebra by my hand, and I should end up with: (1/a)*(1+x/a-r^2/(2*a^2)+(3*x^2)/(2*a^2)+....) in which I only keep up to the 2nd order of r/a (and x/a). I would like to be able to do this by Mathematica. That is, given this sort of a reciprocal of a Sqrt of quadratic expression with x, y and z, I'd like it to expand "approximately" so that a resultant expression only contain the terms up to a specified order of r/a (thus, x/a, y/a, and z/a). How can I do this? This kind of expansion goes on forever, but I don't need many higher order terms. How can I specify the maximum order that I want to have? I will greatly appreciate someone's help to this problem. Meanwhile, I am trying to find a solution in the manual by myself. If you don't mind, please send your solution to my email address: shink at iastate.edu Thank you for your attention.