PHYSICS F./SCI... W/MOD V.II W/KIT
4th Edition
ISBN: 9780134819884
Author: GIANCOLI
Publisher: PEARSON
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Chapter 38, Problem 22P
To determine
The proof that for a particle in a perfectly rigid box, the wavelength of the wave function for any state is the de Broglie wavelength.
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(10) i) Use the quantum mechanical kinetic energy operator T, =
to find the kinetic energy of the first
2m dx?
excited state of the Particle in a Box (with n = 2). ii) Then, use the relationship of kinetic energy and momentum (KE
= p?/2m) to find an equation for the de Broglie wavelength of the particle in a one-dimensional box as a function only
of the box length L and quantum number n. iii) Sketch the wavefunction in the box to verify that the expression you
obtained in part ii) is correct.
(c) Light of wavelength 450 nm is emitted by an electron in an atom behaving as a
lightly damped simple harmonic oscillator with a Q value of 2×107. Find the
natural frequency of the system in radians per second.
(i) We consider a one-dimensional potential barrier problem. In order for the particle to tunnel
through the potential barrier of the width L, the difference between the barrier height U and the
incident energy E of the particle with mass m has to be close. Using the transmission
probability given in the text book / lecture, obtain the energy difference U-E which gives the
transmission probability of exp(-2).
(ii) We consider an infinite square well potential with the width L. Obtain the energy E_{gr} of
the lowest energy level (ground state) of the particle with mass m, and show that E_{gr} scales
linearly with E-U in the problem (i). The potential structures of (i) and (ii) can be viewed as
"shadows" of each other.
Energy
U
---E«
Electron
X
L
L
(iii) We now consider a 3-dimensional infinite square well potential having the length of the x, y, and z
directions to be all L. V=L**3 is the volume of the cube of this potential. We consider energy level of a
single particle (boson)…
Chapter 38 Solutions
PHYSICS F./SCI... W/MOD V.II W/KIT
Ch. 38.3 - Prob. 1AECh. 38.8 - Prob. 1BECh. 38.8 - Prob. 1CECh. 38.9 - Prob. 1DECh. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Would it ever be possible to balance a very sharp...Ch. 38 - Prob. 6Q
Ch. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10QCh. 38 - Prob. 11QCh. 38 - Prob. 12QCh. 38 - Prob. 13QCh. 38 - Prob. 14QCh. 38 - Prob. 15QCh. 38 - Prob. 16QCh. 38 - Prob. 17QCh. 38 - Prob. 18QCh. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10PCh. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46GPCh. 38 - Prob. 47GPCh. 38 - Prob. 48GPCh. 38 - Prob. 49GPCh. 38 - Prob. 50GPCh. 38 - Prob. 51GPCh. 38 - Prob. 52GPCh. 38 - Prob. 53GPCh. 38 - Prob. 54GPCh. 38 - Prob. 55GPCh. 38 - Prob. 56GPCh. 38 - Prob. 57GPCh. 38 - Prob. 58GPCh. 38 - Prob. 59GP
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