5. The Hydrogen-like Atom

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5. The Hydrogen-like Atom
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The energy is quantized.
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????? (5.7) ?????????????? energy value
??????????? Quantum number (n)
?????????????????????? Bohr theory.
1 eV ???????????????????????????????
????????????????????????? 1 Volt
1.602 x 10-19 J
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??? parameter a ???????? Bohr radius of a
hydrogen atom
a Atomic unit , (au)
???????????????? smallest orbit in
the Bohr theory of H
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energy eigenfunction ????????????? quantum
number n , l , m
n 1 , 2 , 3 , principle
quantum number
l 0 , 1 , 2 , , n-1 I m I
azimuthal quantum number (angular
momentum quantum number)
ml 0 , ?1 , ? 2 , , ?l
magnetic quantum number (angular
momentum projection quantum number)
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Normalization of the Hydrogen-like orbitals
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The Time-dependent Wave function of H-atom
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5.2 The Helium Atom
Orbital Approximation 2e- 1 nuclei
Assume nucleus ?????????? (stationary) ?????
2e- ??????? nucleus mnugtgtgtme
1800 ????
Born-Oppenheimer Approximation
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Harmiltonian of a He-like Atom
1 Nucleus ?? z protons ( He z 2 )
2 Electrons ( Li z 3
)
Zero-order Approximation neglecting
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??? probability density ??? normalized
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Indistinguishable of Identical Particle
- e- 2 ?????????????????????? probability
density (5.20) ????? ?????????????
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