Fund Quantum Mechanics Lect & HW Solutions 25

Fund Quantum Mechanics Lect & HW Solutions 25 -...

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Unformatted text preview: 2.2. FUNCTIONS AS VECTORS 2.1.8 7 Solution mathcplx-h Question: Verify that eiα − e−iα /2i = sin α. Answer: Apply the Euler formula for both exponentials and note that sin(−α) = − sin α. 2.2 Functions as Vectors 2.2.1 Solution funcvec-a Question: Graphically compare the spike diagram of the 10-dimensional vector v with components (0.5,1,1.5,2,2.5,3,3.5,4,4.5,5) with the plot of the function f (x) = 0.5x. Answer: vi 5 TT 2.2.2 TT f 5 TT T T TT 5 ¨ 10 ¨¨ ¨¨ ¨¨ 5 i ¨¨ ¨¨ 10 x Solution funcvec-b Question: Graphically compare the spike diagram of the 10-dimensional unit vector ˆ3 , with ı components (0,0,1,0,0,0,0,0,0,0), with the plot of the function f (x) = 1. (No, they do not look alike.) Answer: vi 5 f 5 T 5 10 i 5 10 x ...
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This note was uploaded on 01/06/2012 for the course PHY 3604 taught by Professor Dr.danielarenas during the Fall '11 term at UNF.

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