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Quantum Engi Q and A_Part_3

# Quantum Engi Q and A_Part_3 - 2.2 FUNCTIONS AS VECTORS 7...

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Unformatted text preview: 2.2. FUNCTIONS AS VECTORS 7 2.1.8 Solution mathcplx-h Question: Verify that parenleftBig e i α − e − i α parenrightBig / 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 vectorv with com- ponents (0.5,1,1.5,2,2.5,3,3.5,4,4.5,5) with the plot of the function f ( x ) = 0 . 5 x . Answer: v i 5 5 10 i f 5 5 10 x a8 a8 a8 a8 a8 a8 a8 a8 a8 a8 a8 a54 a54 a54 a54 a54 a54 a54 a54 a54 a54 2.2.2 Solution funcvec-b Question: Graphically compare the spike diagram of the 10-dimensional unit vector ˆ ı 3 , with 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: v i 5 5 10 i f 5 5 10 x a54 8 CHAPTER 2. MATHEMATICAL PREREQUISITES The equivalent of a unit vector for functions is not the function 1, it is the Dirac delta function....
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Quantum Engi Q and A_Part_3 - 2.2 FUNCTIONS AS VECTORS 7...

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