11_Hatom_new

212 ev ground state is 05 energy at this level of

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Unformatted text preview: , 27.212 eV • Ground state is -0.5 • Energy (at this level of approximation) does not depend on the quantum numbers ℓ or , only • Transition energies are just as with Bohr theory Ek En E h nk 1 1 1 EH 2 2 2 n k • When ∞ and 1, the IP is 13.6 eV • Emission to 2 is the Balmer series in the visible • Emission to 1 is the Lyman series in the deep ultraviolet • Emission to 3 is the Paschen series in the infrared Plot a 50% Contour for any H-atom Orbital n 2 l 1 m 0 prinicipal orb. angular momentum projection of l pick the quantum numbers define a general wavefunction s t define associated Laguerre function L( s t x) k 0 2 k 1 k ( s ) ( 1) x ( s t k) ( t k) k l radial wavefunction R( r n l) ( n l 1) 3 2 2 m n 2 n ( ( n l) ) 3 r n l r e L n l 2 l 1 2 r n m define associated Legendre polynomial P( l m x) ( 1) 2 1x l 2 l angular wavefunction, spherical harmonic total wavefunction Y l m ( 2 l 1) ( l m ) 4 ( l m ) 2 d l m l m x2 1 l dx P l m cos exp im n l m r R( r n l) Y l m 12 9/30/2013 plot the wavefunction find rmax and thetamax numerically i i 40 1000 1i i 1000 i 2 Pr R( r n l) R( r n l) r dr i 0 for i 0 1000 imax r i 0 1000 r find rmax associated with 50% contour break if Pr 0.5 imax 117 i rmax r imax rmax 4.68 i find theta at max imax YsY Y 1i 0 l m Y 1i 0 l m i YsYmax max( YsY) YsYmax 0.239 for i 0 1000 break if YsY i YsYmax max 1imax imax 0 max 0 i 2 rmax Y l m sin cos 2 Y max 0 l m Y l m 2 sin sin G rmax 2 Y max 0 l m Y l m 2 cos rmax 2 Y max 0 l m This function takes values of and and maps them into x, y, and z components (stacked in the column vector). The radial value is fixed at the max of the radial probability distribution and the (Y*Y)/(Y*maxYmax) scales to one at the angular max. p CreateMesh ( G 80 80) p Nomencalature 1 2 2 3 3 3 4 4 4 4 ℓ 0 0 1 0 1 2 0 1 2 3 notation 1s 2s 2p 3s 3p 3d 4s 4p...
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This document was uploaded on 01/19/2014.

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