Fund Quantum Mechanics Lect & HW Solutions 66

Fund Quantum Mechanics Lect & HW Solutions 66 -...

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48 CHAPTER 4. SINGLE-PARTICLE SYSTEMS 4.3.1.3 Solution esda-c Question: Continuing this example, what will be the standard deviation? Answer: The average square deviation from 1.5 is: 1 2 (1 1 . 5) 2 + 1 2 (2 1 . 5) 2 = 1 4 Taking a square root, the standard deviation is 0.5. In this case the standard deviation is the same as the maximum deviation, since the deviation from 1.5 is always 0.5 regardless what you throw. 4.3.1.4 Solution esda-d Question: Have I got a die for you! By means of a small piece of lead integrated into its light- weight structure, it does away with that old-fashioned uncertainty. It comes up six every time!
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Unformatted text preview: What will be the expectation value of your throws? What will be the standard deviation? Answer: The expectation value will, of course, be 6, every throw is a 6; 0 1 + 0 2 + 0 3 + 0 4 + 0 5 + 1 6 = 6 , and the standard deviation will, of course, be zero, no throw will deviate from the value 6; σ = [0(1 − 6) 2 + 0(2 − 6) 2 + 0(3 − 6) 2 + 0(4 − 6) 2 + 0(5 − 6) 2 + 1(6 − 6) 2 ] 1 / 2 = 0 4.3.2 Statistics of quantum operators 4.3.2.1 Solution esdb-a Question: The 2p x pointer state of the hydrogen atom was deFned as 1 √ 2 ( − ψ 211 + ψ 21 − 1 ) ....
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