PHYSICS F./SCI... W/MOD V.II W/KIT
4th Edition
ISBN: 9780134819884
Author: GIANCOLI
Publisher: PEARSON
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Chapter 38, Problem 27P
To determine
The lowest four energy levels and wave functions for an electron trapped in an infinitely deep potential well of width
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(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)…
(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
A particle in one-dimension is in the potental
if xl
If there is at least one bound state, the minimum depth of the potential is:
(a)
8ml?
(b)
2ml?
2h?n?
(c)
me?
(d)-
me?
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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- A 6.0-eV electron impacts on a barrier with height 11.0 eV. Find the probability of the electron to tunnel through the barrier if the barrier width is (a) 0.80 nm and (b) 0.40 nm.arrow_forward7) A particular laser oscillating at the resonant wavelength of 1 um has a M value of 1010. The photon number in the cavity at the threshold pumping rate is (Write the Answer as an integral number without using exponents)arrow_forwardIf in a box with infinite walls of size 2 nm there is an electron in the energy state n=1, find its (a) probability density, (b) the wave function and (c) the corresponding energy.arrow_forward
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