Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 10.3, Problem 10.7P
To determine
Obtain the partial wave phase shift for S-wave due to the scattering from a delta function shell given in problem 10.4.
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Subject is physical chemistry. Normalize the two functions and show they are orthogonal.
Problem 9.20
(a) Show that the skin depth in a poor conductor (σ << we) is (2/0)√√√ε/μ (inde-
pendent of frequency). Find the skin depth (in meters) for (pure) water. (Use the
static values of ε, μ, and σ; your answers will be valid, then, only at relatively
low frequencies.)
(b) Show that the skin depth in a good conductor (σ » we) is λ/2л (where λ is the
wavelength in the conductor). Find the skin depth (in nanometers) for a typical
metal (σ 107 (2 m)¯¹) in the visible range (w≈ 10¹5/s), assuming € ≈ €0 and
μ≈μo. Why are metals opaque?
(c) Show that in a good conductor the magnetic field lags the electric field by 45°,
and find the ratio of their amplitudes. For a numerical example, use the "typical
metal" in part (b).
Show that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator
1. Compute T(hat)*psi
2. Compute Vhat* psi - assume V operator is 1/2w^2x^2
3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true
4. From cancellation find a
5. insert back a to Schrodinger eq above and find E
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