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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Question
Chapter 40, Problem 18P
(a)
To determine
The wave function and probability density for
(b)
To determine
The sketch of the wave functions and probability densities.
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Students have asked these similar questions
A single electron of mass m can move freely along a one-dimensionl gold
nanowire. Let x be the position coordinate of the electron along the wire.
(a) Let ø (x) be the wave function of the electron. The quantity |ø (x)|
has dimensions of inverse length. Explain very briefly the meaning
of this quantity as a probability density.
(b) Let us assume that
$ (x) = A sin (3kox)
(2)
where A and ko are fixed, positive constants. Establish whether this
wave function represents an eigenstate of momentum p. Justify your
answer.
Hint: the momentum operator is p
-ih.
-
(c) Establish whether the wave function (x) given in Eq. (2) represents
an eigenstate of kinetic energy K. Justify your answer.
Hint: the kinetic energy operator is K = p²/2m.
(d) Let us now assume that the gold nanowire mentioned above is not
infinite, but extends over a finite length from r= 0 to x = L. Inside
this region, the potential energy of the electron is zero, but outside
this region the potential energy is infinite…
Consider a particle trapped in a 1D box with zero potential energy with walls at x = o
and x = L. The general wavefunction solutions for this problem with quantum number,
n, are:
V,6) = sin )
4n(x) =
The corresponding energy (level) for each wavefunction solution is:
n²h?
En
8mL?
a) What is the probability of finding the particle between x = L/4 and x = 3L/4 when
the particle is in quantum state n = 1, 2 and 3.
You can use calculator or a numerical program to do the integral. For people who want
to try doing the integral by hand, the following identity will be helpful: sin²(x) = (1 – cos
(2x))/2.
radial function of the figure
a) r value at which the probability density is maximum.
b) Find <r>, <r2> and <1 / r>.
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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