Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 6, Problem 54CE
To determine
To show:
The rough average time is
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PROBLEM 3. Using the variational method, calculate the ground state en-
ergy Eo of a particle in the triangular potential:
U(r) = 0 r 0.
Use the trial function
v(x) = Cx exp(-ar),
where a is a variational parameter and C is a normalization constant to
be found. Compare your result for Eo with the exact solution, Eo
1.856(h? F/m)/3.
Demonstrate that e#ikz are solutions to both H and p, (momentum) for a free particle. Do you expect a
difference for a bound particle where V (z) + 0?
Problem 1:
(a) A non-relativistic, free particle of mass m is bouncing back and forth between two perfectly reflecting
walls separated by a distance L. Imagine that the two oppositely directed matter waves associated with this
particle interfere to create a standing wave with a node at each of the walls. Find the kinetic energies of the
ground state (first harmonic, n = 1) and first excited state (second harmonic, n = 2). Find the formula for
the kinetic energy of the n-th harmonic.
(b) If an electron and a proton have the same non-relativistic kinetic energy, which particle has the larger
de Broglie wavelength?
(c) Find the de Broglie wavelength of an electron that is accelerated from rest through a small potential
difference V.
(d) If a free electron has a de Broglie wavelength equal to the diameter of Bohr's model of the hydrogen
atom (twice the Bohr radius), how does its kinetic energy compare to the ground-state energy of an electron
bound to a Bohr model hydrogen atom?
Chapter 6 Solutions
Modern Physics
Ch. 6 - Prob. 1CQCh. 6 - Prob. 2CQCh. 6 - Prob. 3CQCh. 6 - Prob. 4CQCh. 6 - Prob. 5CQCh. 6 - Prob. 6CQCh. 6 - Prob. 7CQCh. 6 - Prob. 8CQCh. 6 - Prob. 9CQCh. 6 - Prob. 10CQ
Ch. 6 - The diagram below plots (k) versus wave number for...Ch. 6 - Prob. 12CQCh. 6 - Prob. 13ECh. 6 - Prob. 14ECh. 6 - Prob. 15ECh. 6 - Prob. 16ECh. 6 - Prob. 17ECh. 6 - Prob. 18ECh. 6 - Prob. 19ECh. 6 - Prob. 20ECh. 6 - Prob. 21ECh. 6 - Prob. 22ECh. 6 - Prob. 23ECh. 6 - Prob. 24ECh. 6 - Prob. 25ECh. 6 - Prob. 26ECh. 6 - Prob. 27ECh. 6 - Prob. 28ECh. 6 - Obtain the smoothness conditions at the...Ch. 6 - Prob. 30ECh. 6 - Prob. 31ECh. 6 - Jump to Jupiter The gravitational potential energy...Ch. 6 - Prob. 33ECh. 6 - Obtain equation (618) from (616) and (617).Ch. 6 - Prob. 35ECh. 6 - Prob. 36ECh. 6 - Prob. 37ECh. 6 - Prob. 38ECh. 6 - Prob. 39ECh. 6 - Prob. 40ECh. 6 - Prob. 41ECh. 6 - Prob. 42ECh. 6 - Prob. 43ECh. 6 - Prob. 44ECh. 6 - Prob. 45ECh. 6 - Prob. 46ECh. 6 - Prob. 47ECh. 6 - Prob. 48ECh. 6 - Prob. 49ECh. 6 - Prob. 50ECh. 6 - Prob. 51CECh. 6 - Prob. 52CECh. 6 - Prob. 53CECh. 6 - Prob. 54CECh. 6 - Prob. 56CE
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