Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 72E
To determine

To Show:A transition where Δml=±1 corresponds to a dipole moment in the xy -plane, while Δml=0 corresponds to a moment along the z-axis.

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A simple illustration of the variation method is provided by the hydrogen atom in the 1s state. Let us assume a form of the trial wave function ψ=e–br where b is a constant. For hydrogen atom, V=-e2/r, so the Hamiltonian operator is Ĥ=-h2/8π2m V2- e2/r.The energy depends on r for the 1s state of the hydrogen atom so the angular portion of the Laplacian can be omitted and replaced by the factor 4π after integration. Therefore, the radial portion of V2=1/r2 (∂/∂r) r2 ∂/∂r.  Solve the energy minimum of the hydrogen atom, E = -2π2 me4/h2.
Consider a hydrogen atom and a singly ionized helium atom. Which atom has the lower ground state energy? (a) Hydrogen (b) Helium (c) The ground state energy is the same for both. Why?
Calculate the radial probability density P(r) for the hydrogen atom in its ground state at (a) r= 0, (b) r = a, and (c) r = 2a, where a is the Bohr radius.

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