This problem develops a basic idea on perturbation theory to the helium atom,)we should evaluate the integral evaluating two-electron integrals. in applying first-order l시간의존성 2 e e1) 4 te vi,(r)w,(r,) i2 x- where 1/2 exp(-zr, /a,) vi(r,) 2 for the helium atom. let us do this integral. and z 11 (a) let ri and r be the radius vectors of electron 1 and 2, respectively, and let 0 be the angle between these two vectors. now this is generally radius vectors, say ri to be the z axis, then the two 0s are the same. using the law of cosines, not the 0 of spherical coordinates, but if we choose one of the ki12=72--2 cos show that e) becomes z6 872 4te -2zrla dre 2zr/dg dre/ 7 ec) 62 j0 desin '(r+2nr, cos 0) 1/2 (hint: there are also integrals over (b) letting x cos 0, show that the integral over 0is desin dx 1c -l 1/2 (+7 cos ) (r+-2n 1/2 (c) substituting this result into e), show that e2 16z6 7 -2zr 7 dre -dre22 ea) 6 4te e2 4z3 1 e -2zq/4 -2zn dre22 + 3 4te a e2 -z 8 4tee ao 2/k2/4 11