Suppose a quanton's wavefunction at a given time is Psi(x) = Ae^-1/2 (x/a)^2, where A is an unspecified constant and a = 1.5 nm. According to my table of integrals, integral_-infinity^infinity [e^-(x/a)^2]dx = a Squareroot pi If we perform an experiment to locate the quanton at this time, what would be the probability of a result within plusminus 0.1 nm of the origin?

Suppose a quanton's wavefunction at a given time is Psi(x) = Ae^-1/2 (x/a)^2, where A is an unspecified constant and a = 1.5 nm. According to my table of integrals, integral_-infinity^infinity [e^-(x/a)^2]dx = a Squareroot pi If we perform an experiment to locate the quanton at this time, what would be the probability of a result within plusminus 0.1 nm of the origin?

Inquiry into Physics

8th Edition

ISBN:9781337515863

Author:Ostdiek

Publisher:Ostdiek

Chapter10: Atomic Physics

Section: Chapter Questions

Problem 23Q

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Suppose a quanton's wavefunction psi(x) at a given time is shown below, where A is an unspecified constant and a = 1.5 nanometers. My table of integrals shows the result below. If we perform an experiment to locate the quanton at this time, what would be the probability of a result within +/- 0.1 nanometers of the origin? (Hint: note that 0.1 nanometers is pretty small compared to the range over which the exponential varies significantly. You should not therefore have to actually calculate an integral.) (Hint: the answer is 7.5%)
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