Lecture_16

Lecture_16 - PHYS 342 ll 2011 Fall 2011 Lecture 16: The...

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Unformatted text preview: PHYS 342 ll 2011 Fall 2011 Lecture 16: The Wavefunctions for tomic Hydrogen Atomic Hydrogen e- , m U(r ) Lecture 16 Understanding the allowed energies 2 2 2 2 2 2 1 1 1 1 13.6 e e e V E m m c 2 2 2 2 2 4 2 ' 1 2 integer 0; 0 1 e e o n n n e n 1,2,... integer 0; 0 1 4 ( , , ) ( ) ( , ) o l m n l l m n n c r R r Y , , , , n l m n l l m n ℓ m 1 2 0,1 [0], [-1, 0, +1] 3 0,1,2 [0], [-1, 0, +1], [-2, -1, 0, +1, +2] etc. = ∞ The energy spectrum allowed n, ℓ ,m (3,0,0); (3,1,-1); (3,1,0); (3,1,-1); n= ∞ (3,2,-2); (3,2,-1); (3,2,0); (3,2,1); (3,2,2) n=3 E=-1.5 eV 0 0); (2 1 1); (2 1 0); =2 = 4 V (2,0,0); (2,1,1); (2,1,0); (2,1,-1) n=2 E=-3.4 eV (1,0,0) - ground state E=-13.6 eV n=1 Degeneracy is a Simple Way to Learn Something About a Complicated System arge collection of Large collection of objects; What are energies? E 1 E 2 E 3 E 4 E 5 E 6 E 7 E 8 E 9 ……… 3 clicks What’s it mean? - for example, onsider the n=2 state 0 0); (2 1 1); (2 1 0); (2 1 - uantum numbers: consider the n=2 state (2,0,0); (2,1,1); (2,1,0); (2,1, 1) Quantum numbers Energy : 2 2 13.6 3.4 n eV E e V 2,0,0 2,0 0,0 ( , , ) ( ) ( , ) r R r Y Wavefunctions: n 2,1,1 2,1 1,1 2,1,0 2,1 1,0 ( , , ) ( ) ( , ) ( , , ) ( ) ( , ) r R r Y r R r Y 2,1, 1 2,1 1, 1 ( , , ) ( ) ( , ) r R r Y Degeneracy: 2 4 n Letter codes to specify the angular wavefunctions ℓ = 1 2 3 code s p d f 2,0, 2 , ,0 ( , , ) ( ) ( , ) r R r Y 2s...
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This note was uploaded on 12/08/2011 for the course PHYS 342 taught by Professor Staff during the Fall '08 term at Purdue.

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Lecture_16 - PHYS 342 ll 2011 Fall 2011 Lecture 16: The...

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