INTRODUCTION I have decided to do a project on how to ...

The helium a<strong>to</strong>m, as depicted in below is a three−particle system which consist of twoelectrons and a nucleus whose mass is 4.0026 amu (6.6461*10 −24 g) and whose charge is+2e. I will assume that here, just as in the treatment of the hydrogen a<strong>to</strong>m, the <strong>to</strong>talSchrodinger equation may be separated in<strong>to</strong> two equations, one involving thetranslational energy of the a<strong>to</strong>m and the other involving the relative motion of theelectrons and the nucleus. I will ignore the translation energy associated with the motionof the centre of mass of the a<strong>to</strong>m in space and will concentrate my attention on therelative motion of particles within the a<strong>to</strong>m and on the energy of the relative motion.Furthermore, in my treatment of relative motion, I will assume that the nucleus isstationary. Although this is no exactly true, the mass of the nucleus is so much larger(about four thousand times larger) than the combined mass of the electrons that theresultant error is not significant.zElectron 2( x2 , y2, z2)1r 2r 12(1 1,1)Electron 1x , y z1r 1ynucleusx1. The potential energy of attraction between the first electron and the nucleus, −2e 2 /r 1 ,where r 1 is the distance between the first electron and the nucleus.2. The potential energy of attraction between the second electron and the nucleus,−2e 2 /r 2 , where r 2 is the distance between the second electron and the nucleus.3. The potential energy of repulsion between the two electrons +e 2 /r 12 , where r 12 is thedistance between two electrons.2