Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Question
Chapter 6, Problem 19E
(a)
To determine
To show: The probability density to the left of the step is
(b)
To determine
The angle and the direction coefficient of the transmitted wave.
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1 W:0E
Problem 1.17 A particle is represented (at time t = 0) by the wave function
| A(a? – x²). if -a < x < +a.
0,
Y (x, 0) =
otherwise.
(a) Determine the normalization constant A.
(b) What is the expectation value of x (at time t =
0)?
(c) What is the expectation value of p (at time t = 0)? (Note that you cannot
get it from p =
md(x)/dt. Why not?)
(d) Find the expectation value of x².
(e) Find the expectation value of p?.
(f) Find the uncertainty in x (ox).
In a scattering experiment, the potential is spherically symmetric and the particles are scat-
tered at such energy that only s and p waves need be considered. If the differential cross-section o (0)
can be written in the form o (0) = a+bcos0+ccos? 0 , then what are the values of a, b, c in the terms of
phase shifts? What is the value oftotal cross-section in terms ofa, b, c?
Consider a beam of particles of kinetic energy E incident on a potential step at x = 0
that is U high, such that E > U, as illustrated in the accompanying figure.
Energy
E
Region I
x = 0
E-U
Region II
|²
1+r
Derive the equation for the reflection probability, R = |^|2 = (+7) 2.
where
KII
k1
r , where A+ and A_ are the amplitudes of the incoming and reflected waves,
k
respectively, and K is the wavenumber in the specified region.|
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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- Problem 1. Using the WKB approximation, calculate the energy eigenvalues En of a quantum- mechanical particle with mass m and potential energy V (x) = V₁ (x/x)*, where V > 0, Express En as a function of n; determine the dimensionless numeric coefficient that emerges in this expression.arrow_forwardIt is stated without proof with respect to Bragg’s law that when the atoms are not sym- metrically disposed to the incident and reflected beams (Fig. 8.3(b)), the path difference (AB + BC) = 2dhkl sin θ . Prove, using very simple geometry, that this is indeed the case.arrow_forwardConsider the wave function for the ground state harmonic oscillator: m w1/4 e-m w x2/(2 h) A. What is the quantum number for this ground state? v = 0 B. Enter the integrand you'd need to evaluate (x) for the ground state harmonic oscillator wave 'function: (x) = |- то dx e C. Evaluate the integral in part B. What do you obtain for the average displacement? 0arrow_forward
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