Mathematic Methods HW Solutions 62

Mathematic Methods HW Solutions 62 - Chapter 13 62 5.14 u =...

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Unformatted text preview: Chapter 13 62 5.14 u = 50 ln r ln 2 + 200 summationdisplay odd n r n- r- n n (2 n- 2- n ) sin n 5.15 u = 50 parenleftbigg 1- ln r ln 2 parenrightbigg- 200 summationdisplay odd n 1 n (2 n- 2- n ) bracketleftbigg parenleftBig r 2 parenrightBig n- parenleftBig r 2 parenrightBig- n bracketrightbigg sin n 6.2 The first six frequencies are 10 , 11 = 1 . 593 10 , 12 = 2 . 135 10 20 = 2 . 295 10 , 13 = 2 . 652 10 , 21 = 2 . 917 10 . 6.4 nm = v 2 radicalBigg parenleftbigg l a parenrightbigg 2 + parenleftBig m b parenrightBig 2 + parenleftBig n c parenrightBig 2 6.5 z = 64 l 4 6 summationdisplay odd m summationdisplay odd n 1 n 3 m 3 sin nx l sin my l cos v ( m 2 + n 2 ) 1 / 2 t l 6.6 n = sin n x x l sin n y y l e- iE n t/ h , E n = 2 h 2 ( n x 2 + n y 2 ) 2 ml 2 6.7 See Problem 6.3. Some other examples of degeneracy: ( n x ,n y ) = (1 , 8) , (8 , 1), (4 , 7) , (7 , 4), giving E n = 65 2 h 2 2 ml 2 ; similarly 2 2 + 9 2...
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