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ENGINEERING PHYSICS - EXAMPLE 30.3 : (a) The quantum number m is given by m = -s, -s + 1. If s = 0.5, find the values of m. (b) | T > = (cos T) | V > + (sin T) | H >. The V and H states form a basis for all polarizations. Let cos T = 0.8. (i) If (sin T)(sin T) + (cos T)(cos T) = 1, find the value of sin T. (ii) For | T > = a | V > + b | H >, where a x a represents the probability of | V > and b x b represents the probability of | H >. Which one is more abundant, | V > or | H >? (iii) Find the value of T without using any mathematical tools.
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ENGINEERING PHYSICS - ANSWER 30.3 : (a) When s = 0.5, m = -s = -0.5 and m = -s + 1 = -0.5 + 1 = 0.5. (b)(i)(sin T)(sin T) = 1 - (cos T)(cos T) = 1 - 0.8 x 0.8 = 0.36. Then sin T = 0.6. (ii) Let a = cos T = 0.8, probability of | V > = a x a = 0.8 x 0.8 = 0.64 (more abundant) and b = sin T = 0.6, probability of | H > = b x b = 0.6 x 0.6 = 0.36 (less abundant). (iii) cos T = 0.8, then T = arc cos 0.8. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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