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1D GaAs semiconductor nanowire with a length L = 2 µm. (A) What is the standard deviation Incertainty) in the velocity of the electron in the conducting band of the nanowire if the ncertainty in its position is 100 pm? (B) At time, t = 0 seconds, we perform a measurement on electron the nanowire, and we found it to be somewhere within a 2 nm interval, i.e., −1 nm > < 1 nm. If we allow the particle to move along the nanowire conduction band, where will we kely find the electron, i.e., what is Axt, at t= 10 ps? What about at t = 1 ns? [Hint: velocity, v =

1D GaAs semiconductor nanowire with a length L = 2 µm. (A) What is the standard deviation Incertainty) in the velocity of the electron in the conducting band of the nanowire if the ncertainty in its position is 100 pm? (B) At time, t = 0 seconds, we perform a measurement on electron the nanowire, and we found it to be somewhere within a 2 nm interval, i.e., −1 nm > < 1 nm. If we allow the particle to move along the nanowire conduction band, where will we kely find the electron, i.e., what is Axt, at t= 10 ps? What about at t = 1 ns? [Hint: velocity, v =

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[Heisenberg Uncertainty Principle] In this problem we will consider an electron in

a 1D GaAs semiconductor nanowire with a length L = 2 µm. (A) What is the standard deviation (uncertainty) in the velocity of the electron in the conducting band of the nanowire if the uncertainty in its position is 100 pm? (B) At time, t = 0 seconds, we perform a measurement on an electron the nanowire, and we found it to be somewhere within a 2 nm interval, i.e., -1 nm > x < 1 nm. If we allow the particle to move along the nanowire conduction band, where will we likely find the electron, i.e., what is Axt, at t = 10 ps? What about at t = 1 ns? [Hint: velocity, v = dx/dt]
Transcribed Image Text:a 1D GaAs semiconductor nanowire with a length L = 2 µm. (A) What is the standard deviation (uncertainty) in the velocity of the electron in the conducting band of the nanowire if the uncertainty in its position is 100 pm? (B) At time, t = 0 seconds, we perform a measurement on an electron the nanowire, and we found it to be somewhere within a 2 nm interval, i.e., -1 nm > x < 1 nm. If we allow the particle to move along the nanowire conduction band, where will we likely find the electron, i.e., what is Axt, at t = 10 ps? What about at t = 1 ns? [Hint: velocity, v = dx/dt]
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