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3502_15_octo14_LG.4

3502_15_octo14_LG.4 - 15-6 The Hydrogenic One-Electron Wave...

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15-6 The Hydrogenic One-Electron Wave Functions Complex form Real (spherical) form Real (cartesian) form a Nomenclature Z 3 /2 ! e " Zr (same as complex) (same as complex) Ψ 100 ; 1s Z 3/2 4 2 " 2 # Zr ( ) e # Zr /2 (same as complex) (same as complex) Ψ 200 ; 2s Z 5/ 2 8 " r sin # e $ i % e $ Zr / 2 Ψ 21–1 ; 2p –1 Z 5 /2 4 2 ! r sin " sin # e $ Zr /2 Z 5 /2 4 2 ! ye " Zr / 2 Ψ 21sin φ ; 2p y Z 5 /2 4 2 ! r cos " e # Zr / 2 (same as complex) Z 5 /2 4 2 ! ze " Zr / 2 Ψ 210 ; 2p z Z 5 /2 4 2 ! r sin " cos # e $ Zr /2 Z 5 /2 4 2 ! xe " Zr / 2 Ψ 21cos φ ; 2p x Z 5/ 2 8 " r sin # e i $ e % Zr / 2 Ψ 211 ; 2p –1 Z 3/ 2 81 3 ! 27 " 18 Zr + 2 Zr ( ) 2 [ ] e " Zr / 3 (same as complex) (same as complex) Ψ 300 ; 3s Z 5/ 2 81 " 6 # Zr [ ] r sin $ e # i % e # Zr / 3 Ψ 31–1 ; 3p –1
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15-7 2 Z 5/ 2 81 ! 6 " Zr ( ) r sin # sin $ e " Zr /3 2 Z 5/ 2 81 ! 6 " Zr ( ) ye " Zr / 3 Ψ 31sin φ ; 3p y 2 Z 5/ 2 81 ! 6 " Zr ( ) r cos # e " Zr /3 (same as complex) 2 Z 5/ 2 81 ! 6 " Zr ( ) ze " Zr / 3 Ψ 310 ; 3p z 2 Z 5/ 2 81 ! 6 " Zr ( ) r sin # cos $ e " Zr /3 2 Z 5/ 2 81 ! 6 " Zr ( ) xe " Zr / 3 Ψ 31cos φ ; 3p x Z 5/ 2 81 " 6 # Zr [ ] r sin $ e i % e # Zr / 3 Ψ 311 ; 3p 1 Z 7/ 2 162 " r 2 sin 2 # e $ 2 i % e $ Zr / 3 Ψ 32–2 ; 3d –2 Z 7 / 2 81 2 ! r 2 sin 2 " sin2 # e $ Zr / 3 Z 7 / 2 81 2 ! xye " Zr / 3 Ψ 31sin2 φ ; 3d xy Z 7/ 2 81 " r 2 sin # cos # e $ i % e $ Zr / 3 Ψ 32–1 ; 3d –1 2 Z 7 /2 81 ! r 2 sin " cos " sin # e $ Zr / 3 2 Z 7 /2
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