By Bilenky, Hosek.

Within the first a part of the evaluation we expound intimately the unified conception of susceptible and electromagnetic interactions of Glashow, Weinberg and Salam within the moment half, at the foundation of this idea a few of the impartial present precipitated procedures are mentioned We think about intimately the deep inelastic scattenng of neutnnos on nucleons, the P-odd asymmetry within the deep inelastic scattering of longitudinally polarized electrons by means of nucleons, the scattenng of neutnnos on electrons, the elastic scattenng of neutnnos on nucleons, and the electron-positron annihilation into leptons

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We now give a few further examples by specifying the nature of the potential energy V. (a) The one-dimensional harmonic oscillator If m is the mass of the oscillator of force constant k, then the Hamiltonian is 2 2 kx2 ^ ¼ À h r þ H 2m 2 ð1:62Þ (b) The atomic one-electron problem (the hydrogen-like system) If r is the distance of the electron of mass m and charge Àe from a nucleus of charge þZe (Z ¼ 1 will give the hydrogen atom), then the Hamiltonian in SI units6 is 2 2 1 Ze2 ^ ¼À h r À H 4p«0 r 2m ð1:63Þ To get rid of all fundamental physical constants in our formulae we shall introduce consistently at this point a system of atomic units7 (au) by posing ð1:64Þ e ¼ h ¼ m ¼ 4p«0 ¼ 1 The basic atomic units of charge, length, energy, and time are expressed in SI units as follows: 8 > charge; e e ¼ 1:602 176 462 Â 10 À 19 C > > > > > h2 > > > length; Bohr a ¼ 4p« ¼ 5:291 772 087 Â 10À11 m 0 0 > 2 > me > < 1 e2 > energy; Hartree Eh ¼ ¼ 4:359 743 802 Â 10À18 J > > 4p« a > 0 0 > > > > h > > > ¼ 2:418 884 331 Â 10À17 s time t¼ > : Eh ð1:65Þ 5 The quantities observable in physical experiments must be real.

28) is divergent at jxj ¼ 1, so that once again the series must be truncated to a polynomial. 29) vanishes, then ðk þ mÞðk þ m þ 1Þ À l ¼ 0 ð3:31Þ giving6 l ¼ ðk þ mÞðk þ m þ 1Þ k; m ¼ 0; 1; 2; . . ð3:32Þ k þ m ¼ ‘ a non-negative integer ð‘ ! 0Þ ð3:33Þ Posing we obtain ‘ ¼ m; m þ 1; m þ 2; . . ‘ ! jmj À‘ m ‘ ð3:34Þ and we recover the well-known relation between angular quantum ^2 numbers ‘ and m. Hence, we obtain for the eigenvalue of L l ¼ ‘ð‘ þ 1Þ ð3:35Þ ‘ ¼ 0; 1; 2; 3; . . ; ðn À 1Þ ð3:36Þ m ¼ 0; Æ1; Æ2; Æ3; .

0Þ ð3:33Þ Posing we obtain ‘ ¼ m; m þ 1; m þ 2; . . ‘ ! jmj À‘ m ‘ ð3:34Þ and we recover the well-known relation between angular quantum ^2 numbers ‘ and m. Hence, we obtain for the eigenvalue of L l ¼ ‘ð‘ þ 1Þ ð3:35Þ ‘ ¼ 0; 1; 2; 3; . . ; ðn À 1Þ ð3:36Þ m ¼ 0; Æ1; Æ2; Æ3; . . 25) 6 Remember that we are using m for |m| ! 0. 40 ATOMIC ORBITALS "ð‘ À mÞ=2 X Q‘m ðxÞ ¼ ð1 À x2 Þm=2 a2k x2k þ ð‘ À X m À 1Þ=2 k¼0 # a2k þ 1 x2k þ 1 ð3:38Þ k¼0 where the first term in brackets is the even polynomial and the second term is the odd polynomial, whose degree is at most kmax ¼ ‘ À mð!