ECTION 11.8 (Atomic Selection Rules) 11.13 When a quantum wave function V is complex (with without makr t appro Eq (1149) to find dr dt, the shrinks, as a function ofr. and classical aton to collapse entircly 11.26 The general pre beyond our scope, cial cases. (a) It s i() - Rrne both real and imaginary parts), its probability density where is the absolute value of V, defined by Eq (612) as -V + V Prove that dr where V is the complex conjugate of *The complex conjugate of any complex wmber x+ iy, where r and y are real, is delined as Xiy) dr dt SECTION 11.4 (More Quantum Formalism ") 11.16 The Hamiltonian operator is often described as a [This property is otten wave function has pari functions listed in Table wave functions with F a of a radiative transition by (11 45), which now takes 4 The outermost (valence) clectron of sodium is in a state when the atom is in its ground state Table 10.2 m Section 10.7) The valence clectron can caded to higher levels, the first few of which are hv in Fig 11.22 Given the selection rule that only trannitions for which Al -tl are allowed, in- m this enery-level diagram all allowed transi- linear operator because it has the lincar property that HAx) + Bex)- AH(x) + BH6() for any two functions x) and dx) and any two consta numbers A and B Prove that the one-dimensional Hamiltonian (11 11) as lunear 11.17 Show that the wave functions (11.21) for th nite square well satisfy the orthoganality properts that (x) o.(4)d-0 for m ws ahong the levels shown, P(n,I,mn, ,m) x SECTION 11.5 (Transitions; Time-Dependent Perturbation Theory ") (This is for radiation po tion. For isotropic average over th sions with ty ( diation can cause transitions bezween these /we cis? What sort of radigtion is this? (visible, U (b) Answer the same questions for the (wee in hydrogen, which are shown in He 7 d 4.5x 10 eV apart. (This is the fine-structorr honatomic eas ba 11.18 (a) The first excited state of the sodm 211 eV above the ground state What waveleng ra ting discussed in Section 9.7) (c) Answer the er goestious for the lowest Iwo levels of the Li which are 048 McV ápart. WARE I1 22 n di any one