Suppose Fuzzy, a quantum-mechanical duck, lives in a world in which h = 2 ? J So

Question

Suppose Fuzzy, a quantum-mechanical duck, lives in a world in whichh= 2?J

Explanation / Answer

According to the Uncertainty Principle: ?x*?p > ?/2 ? = h/2? Since h = 2?J*s, ? = h/2? = 2?J*s / 2? = 1 J*s Thus the Uncertainty Principle in Fuzzy's Universe is: ?x*?p > 1/2 J*s a) From the initial conditions: ?x = 1.00 m ?p = m?v = 1.80kg * ?v Given: ?x*?p > 1/2 J*s 1.00 m * 1.80kg * ?v > 1/2 J*s ?v > 1/2 J*s / (1.00 m * 1.80kg) ?v > 0.277777778 m/s b) ?x*?p > 1/2 J*s ?p = m*?v = 1.80kg * 0.277777778 m/s = 0.500 m*kg/s ?x > 1/2 J*s / ?p ?x > 1/2 J*s / 0.500 m*kg/s ?x > 1.00 m Answer: a) 0.278 m/s b) 1.00 m

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