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
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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[Ã (x)]=Ã(x) +Ã (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,?
Chapter 40 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 40.1 - Prob. 40.1QQCh. 40.2 - Prob. 40.2QQCh. 40.2 - Prob. 40.3QQCh. 40.5 - Prob. 40.4QQCh. 40 - Prob. 1PCh. 40 - Prob. 2PCh. 40 - Prob. 3PCh. 40 - Prob. 4PCh. 40 - Prob. 5PCh. 40 - Prob. 6P
Ch. 40 - Prob. 7PCh. 40 - Prob. 9PCh. 40 - Prob. 10PCh. 40 - Prob. 11PCh. 40 - Prob. 12PCh. 40 - Prob. 13PCh. 40 - Prob. 14PCh. 40 - Prob. 15PCh. 40 - Prob. 16PCh. 40 - Prob. 17PCh. 40 - Prob. 18PCh. 40 - Prob. 19PCh. 40 - Prob. 20PCh. 40 - Prob. 21PCh. 40 - Prob. 23PCh. 40 - Prob. 24PCh. 40 - Prob. 25PCh. 40 - Prob. 26PCh. 40 - Prob. 27PCh. 40 - Prob. 28PCh. 40 - Prob. 29PCh. 40 - Two particles with masses m1 and m2 are joined by...Ch. 40 - Prob. 31APCh. 40 - Prob. 32APCh. 40 - Prob. 33APCh. 40 - Prob. 34APCh. 40 - Prob. 36APCh. 40 - Prob. 37APCh. 40 - Prob. 38APCh. 40 - Prob. 39APCh. 40 - Prob. 40APCh. 40 - Prob. 41APCh. 40 - Prob. 42APCh. 40 - Prob. 44CPCh. 40 - Prob. 46CPCh. 40 - Prob. 47CP
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