The Real Hydrogen Atom

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2 i-obit Itatios A o-o obita agua otu odus a agti fid to ss it. Its agti ot itats givig gy sift i st fa of to, B fid is s book/r: dv B d gsµ b F µ B B us B Av B v ovt bak to ab fa Toas ssio du to o-itia fa givs a fato of Dia q givs dity. gy dds o si-obit ouig g µ b s dv d P6 - a H ato

3 i-obit: Quatu Nubs T si-obit ouig * auss ad s to o og b good quatu ubs if H ψ aso igfutios [ H, ] H H V ad, si-obit itatios ags gy. H H I atoi ysis, sa tubatio, ad a sti us H satia ad si wav futio as vy good statig oit. ag ffts i ua ysis ad wi s gy odig vy difft du to ouigs. o i atoi ust d xtatio vau of additioa itatio : Hψ ψ [, ] [, ] a as x x x, y y, y doot out P6 - a H ato

4 P6 - a H ato xtatio vau Dti xtatio vau of t si-obit itatio usig tubatio toy. Assu J,, a a good quatu ubs wi is t tu assu H wav futio is ~igfutio of tubd ottia [ ], > >< >< < > < J J o J if J, : s s wit vaus fo s s

5 xtatio vau To dti t gy sift, aso d t xtatio vau of t adia ts usig agu oyoias as dv d d ψ ψ * d a ut a t ts togt to gt si-obit gy sift. if, J/, J/ J/ wit ativisti / / P6 - a H ato 5

6 P6 - a H ato 6 Nuoogy av but ad so a a a

7 P6 - a H ato 7 i Obit gy sift Fo P stat. N,, J / o / ad so gy sit btw vs is J/ / V sit sit

8 P6 - a H ato 8 Rativisti ffts ovd usig o-ativisti.. a tat ativisti t K as a tubatio <V> a us viia to 8 8 K T [ ] V V V but V V K V K V K v,,.. ψ ψ a Z Z V o

9 P6 - a H ato 9 Rativistisi-obit ffts by itgatig ov t adia wav futio obi si-obit ad ativisti otios gy vs dd o oy!. Dia quatio givs dity ot as tubatio. Fo av: a Z Z o V 8 Z K [ ] : ± us

10 P6 - a H ato gy vs i Hydog Dgay stosoi otatio: wit stat, P-stat, D-stat aso a ot si doubt is sig to wit s/ N N N,,,, P D P D,, P P # stats

11 Za fft:xta B Fid gy sift dds o ad ovs ay aiig dgay. Now two fids ita ad xta ad dtais of sittig dds o ativ stgts µ b J ad µ wit... ad... Uss, t agti ot ad t tota agua otu a ot i t sa ditio ad a t i B ditio. Fo wak xta fid, aiuatig t dot oduts givs P g B µ B µ b Bg s s B> P6 - a H ato

12 Za fft stog fid -,,- P6 - a H ato

13 Za fft:xta B Fid Assu tat wak B fid if stog t ad wo t ou B fid off oto gy B fid o 6 oto gis wit ti gy ddig o t g fato ad o t B fid O of t fist idiatos tat t to ad itisi agua otu s/ P, s g s gp B B> 5 5 s P6 - a H ato

14 Hyfi ittig May ui aso av si, av /. Mad fo / quaks us additioa quaks ad atiquaks ad guos. G- fatos a 5.58 ad -.8 fo tis - fo to. Nua g-fatos/agti ots oiatd. Usuay ust us xita ub fo Hydog. t I b t ua si / gµ µ I g µ av addd ts to gy. Fo -stats, ad a igo tat t aµ bµ µ u µ B P6 - a H ato

15 Hyfi ittig to si ous to ua si µ µ I sis sis I oosit aigd f f t f f F,, I s s I I i i so gy diff btw sis oosit ad aigd. Givs i fo ydog ad is basis of NMR/MRI [ f f ] 6 6 V P6 - a H ato 5

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