In molecular and solid-state applications, one often uses a basis of orbitals aligned with the cartesian axes
Question:
In molecular and solid-state applications, one often uses a basis of orbitals aligned with the cartesian axes rather than the basis used throughout this chapter. For example, the orbitals
are a basis for the hydrogen states with n = 2 and ℓ = 1.
(a) Show that each of these orbitals can be written as a linear combination of the orbitals Ψnℓm with n = 2, ℓ = 1and m = 1,0,1.
(b) Show that the states Ψ2pi are eigenstates of the corresponding component of angular momentum: L̂i. What is the eigenvalue in each case.
(c) Make contour plots (as in Figure 4.9) for the three orbitals. In Mathematica use ContourPlot3D.
Figure 4.9
ψ2ρ. (r,θ, φ) = Ψ2p, (r,θ, φ) = ψ2p. (r,6,φ) = 1 e V32πα α 1 V32πα α 1 X Ε 32πα3 α -1/2a -¹/2a
Step by Step Answer:
a A similar calculation gives b L z 2pz L z 210 0 since m 0 By cyclic perm...View the full answer
Introduction To Quantum Mechanics
ISBN: 9781107189638
3rd Edition
Authors: David J. Griffiths, Darrell F. Schroeter
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