Fund Quantum Mechanics Lect & HW Solutions 65

Fund Quantum Mechanics Lect & HW Solutions 65 -...

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Unformatted text preview: 4.3. EXPECTATION VALUE AND STANDARD DEVIATION 47 or multiplying out 2px |2px = 1 ( ψ211 |ψ211 + −ψ211 |ψ21−1 + ψ21−1 | − ψ211 + ψ21−1 |ψ21−1 ) 2 or using the orthonormality of ψ211 and ψ21−1 . 2px |2px = 1 (1 + 0 + 0 + 1) = 1. 2 For the state 2py , remember that i comes out of the left side of the inner product as −i: 2py |2py = −i2 ψ211 + ψ21−1 |ψ211 + ψ21−1 2 The rest goes the same way. 4.3 Expectation Value and Standard Deviation 4.3.1 Statistics of a die 4.3.1.1 Solution esda-a Question: Suppose you toss a coin a large number of times, and count heads as one, tails as two. What will be the expectation value? Answer: For a fair coin, the probability of heads or tails is the same; each will have a 1 1 probability of 50% or 2 . So the expectation value is 1 × 1 + 2 × 2 = 1.5. This will be the 2 average value you obtain in a large number of throws. 4.3.1.2 Solution esda-b Question: Continuing this example, what will be the maximum deviation? Answer: If you throw a 1, the deviation is |1 − 1.5| or 0.5. If you throw a 2, the deviation is |2 − 1.5|, also 0.5. So the maximum deviation is 0.5. ...
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This note was uploaded on 01/06/2012 for the course PHY 3604 taught by Professor Dr.danielarenas during the Fall '11 term at UNF.

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