Similarly the other laws also work duly emboldened we

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Unformatted text preview: ø + i sin ø] De Moivre's Theorem now implies that eiøei˙ = ei(ø+˙), so that the exponential rule for addition works, and the inverse rule shows that 1/eiø = e -iø, so that the inverse exponent law also works. Similarly, the other laws also work. Duly emboldened, we now define ex+iy = exeiy = ex[cos y + i sin y] ex+iy = ex[cos y + i sin y] Examples in class Exercise Set 1 p.793 #1–17 odd, 27, 29, 37, 39 p. 797. 1–15 odd, 21, 23, 25, 27, 29, 31, 33 p. 800 #1, 5, 7, 11, 15, 23, 26 Hand In 1 (a) One of the quantum mechanics wave functions of a particle of unit mass trapped in an infinite potential square well of width 1 unit is given by 2 2 §(x,t) = sin(πx) e-i(π h–/2) t + sin(2πx)e-i(4π h–/2) t , where h– is a certain constant. Show that |§(x,t)|2 = sin2πx + sin22πx+ 4sin2πx cosπx cos3ø, where ø = -(π2h/2)t. – (|§(x,t)|2 is the probability density function for the position of the particle at time t.) (b) The expected position of the particle referred to in part (a) is given by 1 Û “x...
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This document was uploaded on 03/20/2014 for the course MATH 144 at Hofstra University.

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