Uncertan

Uncertan - Ground State of the Hydrogen Atom V (eV) 0 z 0.2...

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Ground State of the Hydrogen Atom -80 -70 -60 -50 -40 -30 -20 -10 0 0 0.1 0.2 0.3 r(nm) V(eV) V(r) = -Z e 2 4 π ε o r e = 1.60 x 10 -19 C ε o = 8.85 x 10 -12 J -1 c 2 m -1 x y z θ φ r e h 2 2m 2 Ψ +V Ψ = Ε Ψ h 2 2m 2 x 2 + 2 y 2 + 2 z 2 Ψ + -Z e 2 4 π ε o r Ψ = Ε Ψ 2 = 1 r 2 r 2 r + 1 r 2 Λ 2 Λ 2 = 1 sin 2 θ 2 φ 2 + 1 sin θ θ sin θ θ Ψ= R(r) Θ(θ) Φ(φ) = R(r) Y l, m l –h 2 2mr 2 2 Φ φ 2 = 2 m 2 l 2mr 2 Φ l z =h m l Φ(φ) = 1 2 π 1/2 e im l φ Λ 2 Y l, m l = l ( l +1) Y l, m l h 2 2m 1 r 2 r 2 r R(r) Y l, m l + Λ 2 r 2 R(r) Y l, m l - Ze 2 4 π ε o r R(r) Y l, m l = Ε R(r) Y l, m l h 2 2m Y l, m l 1 r 2 r 2 r R(r) – R(r) l ( l r 2 Y l, m l 2 4 π ε o r R(r) Y l, m l = Ε R(r) Y l, m l h 2 2m
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This document was uploaded on 02/22/2012.

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Uncertan - Ground State of the Hydrogen Atom V (eV) 0 z 0.2...

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