Answer Happy

Exciting hydrogen Consider the optical transition in hydrogen from its ground state to the first excited level (n = 2). Ignore fine and hyperfine structure. You will need the wavefunctions = 3 r V 100 = 2 (1) *exp(-) (4.1) ao ao 1 x ✓ 41 Y: (0,0) R1,0(r) 1 1 r r 3 V210 4'0-(-) Video exp Х cos () (4.2) 2V6 (ao ao 2ao 47 R2,1(r) Yº (0,0) (a) Explain briefly which physical quantities are determined by the quantum numbers 1 and m. State all possible combinations of the quantum numbers 1 and m for the excited level with n=2. {4} (b) Show that the dipole matrix element d12 = e(+210|f · € V100), (4.3) for 7-polarized light, i.e. with polarization vector e = ez, is given by 128V2 d12 (4.4) 243 = . -eao. Hint: Consider the substitution u = cos 0 and use the standard integral n! 6.***exp(-ar)dr = (4.5) an+1' which is valid for integer n > 0 and real a > 0. {11}