Lecture 25 typed

# Lecture 25 typed - 1 Lecture 25 The Internal Structure of...

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Unformatted text preview: 1 Lecture 25: The Internal Structure of the Hydrogen Atom Consider Hydrogenic atoms where the nuclear charge is +Ze, e denoting the charge of an electron. For hydrogen, Z=1. Let m 1 and r 1 denote the mass and position of the nucleus and m 2 and r 2 denote the mass and position of the electron. Then 1 2 | | r r r = − a a is the distance between particles. The Hamiltonian is as follows. Now we begin to work on separating internal (electronic) and external (atomic) motions. The first term in the Hamiltonian represents the KE of the nucleus where the second term represents the KE of the electronic motion. For a hydrogen atom, 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 ˆ 2 2 4 Permittivity of free space The Laplacian Ze H m m r x y z πε ε − = ∇ − ∇ − = ∂ ∂ ∂ ∇ = = + + ∂ ∂ ∂ ℏ ℏ 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 2 2 2 2 2 Let & (center of mass) and reduced mass , Then, and and ˆ Then, 2 2 R R r R m r m r r r r R m m m m M m m m m r R r r R r m m r r r m r m...
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Lecture 25 typed - 1 Lecture 25 The Internal Structure of...

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