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Exam3_Key - Midterm3Key 1(20pts 2!Y 2 0 0 sin d d = 00 0"1...

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Midterm 3 Key 1) (20 pts) Y 0,0 2 0 ! ! 0 2 ! sin " d d = 1 4 " # $ % & 0 ! 0 2 ! 2 sin # d d = 1 4 d sin 0 ! 0 2 ! d = 1 4 ( 2 ( ) cos ( ) 0 = 1 4 ( 2 ( ) ) 1 ( ) ) ) 1 ( ) * + , - = 1 2) (20 pts) Y 1,0 ! cos m = 0 E 1,0 = " B # 0 = 0 Y 1,1 ! sin e i m = 1 E = " B # 1 = " B Y 1, " 1 ! sin e " i m = " 1 E = " B # " 1 ( ) = B Lowest to highest energy: sin e i , cos , sin e " i 3) (20 pts) x , y ( ) = 2 L x sin n x x L x ! " # $ % & 2 L y sin n y y L y ! " # $ % & = 4 L x L y sin n x x L x ! " # $ % & sin n y y L y ! " # $ % & E = ! 2 2 2 m n x 2 L x 2 + n y 2 L y 2 ! " # $ % & 4) (20 pts) n = 4 l = 0, 2, 3 m = 3 2 2 1 1 1 0 ! 1 ! 1 ! 1 ! 2 ! 2 ! 3 Number of states for n=4 is 16.
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5) (20 pts)
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Exam3_Key - Midterm3Key 1(20pts 2!Y 2 0 0 sin d d = 00 0"1...

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