EP PHYSICS F/SCI.+ENGR.W/MOD..-MOD MAST
4th Edition
ISBN: 9780133899634
Author: GIANCOLI
Publisher: PEARSON CO
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Chapter 38, Problem 37P
To determine
The distance outside the walls at which the ground state wave function drops to
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(A) An electron is confined between two impenetrable walls 0.200 nm apart. Determine the energy levels for the states n = 1, 2, and 3.
A particle in one-dimension is in the potental
if xl
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8ml?
(b)
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2h?n?
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me?
(d)-
me?
(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
Chapter 38 Solutions
EP PHYSICS F/SCI.+ENGR.W/MOD..-MOD MAST
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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- (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)…arrow_forwardJC-42) Probability to Find an Electron An electron in its ground state is trapped in the 1D Coulomb potential energy. What is the 0.99ao and x = probability to find it in the region between x = 1.01ao?arrow_forwardWhat would you NOT expect in the limits that the quantum well has infinite width, e.g. quantum confinement goes away? the lowest possible energy will be larger than zero O there will be no wave solution anymore (probability amplitude goes to zero) O energy separation would be zero; and rather than discrete energy levels there will be a continuous energy spectrum O the Correspondence principle will be fulfilledarrow_forward
- JC-33) Particle in a Well A particle is trapped in an infinite one-dimensional well of width L. If the particle is in its ground state, evaluate the probability to find the particle (a) between x = 0 and x = L/3; (b) between x = L/3 and x = 2L/3; (c) between x = 2L/3 and x = L. %3Darrow_forwardCheck Your Understanding Suppose that a particle with energy E is moving along the x-axis and is in the region O and L. One possible wave function is (x,t)={AeiEt/hsinxL, when 0xL otherwise Determine the normalization constant.arrow_forwardA 5.0-eV electron impacts on a barrier of with 0.60 nm. Find the probability of the electron to tunnel through the barrier if the barrier height is (a) 7.0 eV; (b) 9.0 eV; and (c) 13.0 eV.arrow_forward
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