P7D.8* A particle is confined to move in a one-dimensional box of length L. If the particle is behaving classically, then it simply bounces back and forth in the box, moving with a constant speed. (a) Explain why the probability density, P(x), for the classical particle is 1/L. (Hint: What is the total probability of finding the particle in the box?) (b) Explain why the average value of x" is (x")= , P(x)x"dx . (c) By evaluating such an integral, find (x) and (x*). (d) For a quantum particle (x)=L/2 and (x*)=L (}-1/2n°n²). Compare these expressions with those you have obtained in (c), recalling that the correspondence principle states that, for very large values of the quantum numbers, the predictions of quantum mechanics approach those of classical mechanics.

P7D.8* A particle is confined to move in a one-dimensional box of length L. If the particle is behaving classically, then it simply bounces back and forth in the box, moving with a constant speed. (a) Explain why the probability density, P(x), for the classical particle is 1/L. (Hint: What is the total probability of finding the particle in the box?) (b) Explain why the average value of x" is (x")= , P(x)x"dx . (c) By evaluating such an integral, find (x) and (x). (d) For a quantum particle (x)=L/2 and (x)=L (}-1/2n°n²). Compare these expressions with those you have obtained in (c), recalling that the correspondence principle states that, for very large values of the quantum numbers, the predictions of quantum mechanics approach those of classical mechanics.

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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