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A particle in an infinite square well is prepared in the state

A particle in an infinite square well is prepared in the state

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Problem 1.13 A particle in an infinite square well is prepared in the state v(x) = lW1(x) + b2(x)], where 1 and b2 are the ground and first excited states respectively. (See Eq. 1.71.) 1. What is the probability of finding the particle in the ground state of the well? 2. For the state (x), consider the left and right halves of the well sepa- rately, and state whether 1 and 2 interfere constructively or destruc- tively in each half. [Hint: draw b1(x) and Þ2(x) on the same axes.] 3. For the state v(x), is the probability of finding the particle in the left half of the well greater than, equal to, or less than 1/2? Explain your answer in a sentence or two. 4. The energy of a particle in state (x) is measured. What is the prob- ability of finding the particle in the left half of the well if, after the energy measurement, its position is measured? Briefly explain.
Transcribed Image Text:Problem 1.13 A particle in an infinite square well is prepared in the state v(x) = lW1(x) + b2(x)], where 1 and b2 are the ground and first excited states respectively. (See Eq. 1.71.) 1. What is the probability of finding the particle in the ground state of the well? 2. For the state (x), consider the left and right halves of the well sepa- rately, and state whether 1 and 2 interfere constructively or destruc- tively in each half. [Hint: draw b1(x) and Þ2(x) on the same axes.] 3. For the state v(x), is the probability of finding the particle in the left half of the well greater than, equal to, or less than 1/2? Explain your answer in a sentence or two. 4. The energy of a particle in state (x) is measured. What is the prob- ability of finding the particle in the left half of the well if, after the energy measurement, its position is measured? Briefly explain.
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