HydrogenAtomSummary - eigenvalue. Other expectation values...

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Summary of Quantum Solution for the Hydrogen Atom Physics 4605 Spring 2001 Prof. Brian Tonner ( 29 ( 29 l m l n l n Y r R m l nlm - - = = = 1 ,.. 1 , 0 .. 3 , 2 , 1 , φ θ ψ 2 2 0 e a μ = 2 2 0 2 2 6 . 13 2 n eV n a e Z E n - = - = - = - - = - = 0 0 2 / 3 0 21 0 0 2 / 3 0 20 0 2 / 3 0 10 2 exp 3 1 2 2 exp 2 2 exp 2 a Zr a Zr a Z R a Zr a Zr a Z R a Zr a Z R The Radial Probability Density is 2 2 nl r R r P = . The maximum in the Radial Probability Density occurs at ( 29 0 2 max a n r P r = only for the state in which l=n-1. This is a special property of the Coulomb potential, in that the Bohr result and the quantum result agree for the radial probability maximum, and the energy
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Unformatted text preview: eigenvalue. Other expectation values are more complex: ( 29 ( 29 ( 29 2 / 1 1 1 3 / 1 1 1 2 3 1 1 1 2 1 1 3 2 2 2 2 2 2 4 2 2 2 2 + = = -+-+ = +-+ = l n a Z r n a Z r n l l Z n a r n l l Z n a r Number of degenerate states per energy eigenvalue, D =n 2 ....
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This note was uploaded on 08/16/2011 for the course PHY 4605 taught by Professor Leuenberger,m during the Spring '08 term at University of Central Florida.

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HydrogenAtomSummary - eigenvalue. Other expectation values...

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