Physics for Scientists and Engineers, Vol. 1
6th Edition
ISBN: 9781429201322
Author: Paul A. Tipler, Gene Mosca
Publisher: Macmillan Higher Education
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Chapter 35, Problem 38P
To determine
The sketch of shape of the wave system for ground state.
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Find the equilibrium positions of the following 1-dimensional potential energy function. Examine the stability of these positions. Find the classical turning points for E = -W/8.
U(x) = ( -Wd2 (x2 + d2) ) / ( x4 + 8d4 )
Here W and d are positive constants.Help: Use the Z(y) = U(y) / W function after defining the y = x/d auxiliary variable.
What does your result for the potential energy U(x=+L) become in the limit a→0?
Write down the equations and the associated boundary conditions for
solving particle in a 1-D box of dimension L with a finite potential
well, i.e., the potential energy U is zero inside the box, but finite
outside the box. Specifically, U = U₁ for x L. Assuming that particle's energy E is less
than U, what form do the solutions take? Without solving the
problem (feel free to give it a try though), qualitatively compare with
the case with infinitely hard walls by sketching the differences in
wave functions and probability densities and describing the changes
in particle momenta and energy levels (e.g., increasing or decreasing
and why), for a given quantum number.
Chapter 35 Solutions
Physics for Scientists and Engineers, Vol. 1
Ch. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7PCh. 35 - Prob. 8PCh. 35 - Prob. 9PCh. 35 - Prob. 10P
Ch. 35 - Prob. 11PCh. 35 - Prob. 12PCh. 35 - Prob. 13PCh. 35 - Prob. 14PCh. 35 - Prob. 15PCh. 35 - Prob. 16PCh. 35 - Prob. 17PCh. 35 - Prob. 18PCh. 35 - Prob. 19PCh. 35 - Prob. 20PCh. 35 - Prob. 21PCh. 35 - Prob. 22PCh. 35 - Prob. 23PCh. 35 - Prob. 24PCh. 35 - Prob. 25PCh. 35 - Prob. 26PCh. 35 - Prob. 27PCh. 35 - Prob. 28PCh. 35 - Prob. 29PCh. 35 - Prob. 30PCh. 35 - Prob. 31PCh. 35 - Prob. 32PCh. 35 - Prob. 33PCh. 35 - Prob. 34PCh. 35 - Prob. 35PCh. 35 - Prob. 36PCh. 35 - Prob. 37PCh. 35 - Prob. 38P
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