Daily_012.SOLN - are greater than zero when squared.)...

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Phys 274 – c ± Eric B. Szarmes 14 February 2011 Daily Homework 12 SOLUTIONS Problem 1 – Q6T.2 ; Q6T.3 Q6T.2 A: The probability is 0, because the state | ψ i = ± 1 / 2 , 1 / 2 ² is the | + x i state. Therefore, all of the electrons will emerge from the (+) channel of the SG x device (with their spins aligned with + x ), and none will emerge from the ( - ) channel (with spin anti -aligned with + x ). Q6T.3 D: If an electron emerges from the ( - ) channel of the SG z device, its spin state is |- z i = [0 , 1] , independent of what went in. Problem 2 – Q6T.5 ; Q6T.6 Q6T.5 E: The wavefunction has its maximum absolute value at x = 0 (even though it is negative). Therefore, the square of the wavefunction (which determines the probability) is largest at x = 0. Q6T.6 F: The minimum probability is where the square of the wavefunction is a minimum. This occurs where the wavefunction is zero. (Negative values of the wavefunction yield probabilities that
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Unformatted text preview: are greater than zero when squared.) Problem 3 Q6T.7 ; Q6T.8 The wavefunction and its square are shown below. Note that the total area under the squared wavefunction is 12 (little squares), which corresponds to a probability of unity. ! (x) x 1 | ! (x) | 2 x Area = 12 1 Q6T.7 E: If the measurement result yields x > 1 nm, this corresponds to the (darker) shaded area under the squared wavefunction, which has an area of 5 (little squares). Since the total area is 12, the corresponding probability is 5/12. Q6T.8 D: If the measurement result yields-2 nm < x < 0 nm, this corresponds to the (lighter) shaded area under the squared wavefunction, which has an area of 2 (little squares). Again, since the total area is 12, the corresponding probability is 2/12 = 1/6. 1...
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