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quiz6 - Page 1 of 2 Department of Physics University of...

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Page 1 of 2 Department of Physics University of California San Diego Modern Physics (2D) Prof. V. Sharma Quiz # 6 (Feb 18 2005) Some Relevant Formulae, Constants and Identities ! = h p ; " x . " p # h 4 $ ; " E . " t # h 4 $ Time Dependent S. Eq: % ! 2 2 m d 2 & ( x , t ) dx 2 + U ( x ) & ( x , t ) = i ! ’& ( x , t ) t Time Independent S. Eq: % ! 2 2m d 2 ( ( x ) dx 2 + U ( x ) ( ( x ) = E ( ( x ) Particle in box of length L: ( n (0 < x < L ) = 2 L sin n $ x L ) * + , - . & E n = n 2 $ 2 ! 2 2 mL 2 Planck's constant h = 6.626 / 10 -34 J.s=4.136 / 10 -15 eV.s 1 eV = 1.60 / 10 -19 J Electron mass = 9.1 / 10 -31 Kg = 0.511 MeV/c 2 Energy in Hydrogen atom E n = % ke 2 2 a 0 1 n 2 ) * + , - . = % 13.6 eV n 2 ) * + , - . sin 0 sin 1 = 1 2 cos( 0 % 1 ) % cos( 0 + 1 ) ( ) sin 2 x dx = = % 1 2 cos x sin x + 1 2 x = 1 2 x % 1 4 sin2 x 2 Pl. write you answer in the Blue Book in indelible ink. Make sure your code number is prominently displayed on each page. Consult the proctors if you have difficulty understanding the text of a problem.
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Page 2 of 2 Department of Physics University of California San Diego Modern Physics (2D) Prof. V. Sharma Quiz # 6 Problem 1: Designer Wavefunctions ! [ 6 pts] If ! 1 and ! 2 are two solutions of the Time Independent Schrodinger Equation
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