Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 40, Problem 38AP
To determine

Show that x2=L23L22n2π2 for a particle in infinitely deep 1-D box.

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Linear operators play an important role in the quantum mechanical description of matter. Which of the following is true of all linear operators, A and B? A[k f(x)]=kà (x) Ã[à (x)]=Ã(x) +à (x) A[Bf(x)]=B[Ã(x)] ○ AB f(x)=B A f(x)
In quantum mechanics, the probability of finding a particle æ in domain (a, b) can be calculated from the following formula P(a < # < b) = / Mla p(x)dr where the probability density p(a') satisfies p(x) « 1/x for æ e (1, e²) and being 0 elsewhere. Please determine the exact form of the probability density and calculate the probability of finding a particle in domain [1, 2).
Consider a particle of mass m moving in a 2-dimensional rectangular box of sides La and Ly, with Le 2Ly. If we use the symbols E, to denote the energy of the ground state of the system, Ee1 the energy of the first excited state, Ee2 the energy of the second excited state, and Ee3 the energy of the third excited state, what are the numerical values of the ratios Ee1/Eg, Ee2/Eg, and Ee3/E,?
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