INVERSE QUANTUM STATES OF HYDROGEN

Transcription

1 INVERSE QUANTUM STATES OF HYDROGEN Rnald C. Bugin Edgecmbe Cmmunity Cllege Rcky Munt, Nth Calina 780 ABSTRACT The pssible existence f factinal quantum states in the hydgen atm has been debated since the adent f quantum they in 94. Inteest in the tpic has intensified ecently due t the claimed expeimental findings f Randell Mills at Blacklight Pwe, Inc., Canbuy, New Jesey f 37 inese pincipal quantum leels, which he tems the hydin state f hydgen. This pape will shw that the classic wae equatin pedicts exactly that numbe f ecipcal enegy states. INTRODUCTION: Intensie labaty eseach e much f the past decade at Blacklight Pwe and at the Technical Uniesity f Eindhen, see Ref. [] f a eiew, n what has cme t be knwn as the hydin state f hydgen has sent theists scuying t explain the expeimental spectscpic bseatins n the basis f knwn and tusted physical laws. Jan Naudts f the Uniesity f Antwep, f example, ffes the agument that the Klein-Gdn equatin f elatiistic quantum mechanics allws an inese quantum state. Andeas Rathke f the Eupean Space Agency s Adanced Cncepts Team insists that the classic wae equatin cannt pduce squae integable factinal quantum states. Randell Mills f Blacklight Pwe emplys a they based n the Bh cncept f a paticle in bit aund a much heaie cental mass. 3 Based n the esults f the fllwing analysis, Naudts and Mills appea t be ight. Page f 7

2 PRESENTATION: The classic matte wae equatin = t () in spheical cdinates,,, can be witten as + + sin sin sin = t () whee is the matte-wae phase elcity. Calculatin is eased by use f the tansfmatin = cs (3) which pduces a simplified equatin + + = t (4) whee is the distance f the electn fm the nucleus. Suppessin f the time in equatin (4) can be achieed by use f the substitutin = i t e (5) pducing Page f 7

3 + + 0 (6) Sepaatin f the space aiables can be achieed by the ansatz R (7) whee each fact in the pduct is a functin f the aiable epesented. When tansfmatin (7) is used in equatin (6), and the esulting equatin is diided by the pduct gien, pduced is R R R R ( ) ( ) 0 (8) The tem cntaining the equatial angle can be sepaated and shwn t be a cnstant d m d (9) esulting in the diffeential equatin d 0 m d (0) Slutins f equatin (0) ae fund by e im () (except f a multiplying cnstant), whee m is the bital magnetic quantum numbe with alues 0,,, 3,. Page 3 f 7

4 The quantity within baces in equatin (8) can nw be witten as d ( d ) d d m k () which, when bth sides ae multiplied by, yields d d d m k 0 d (3) Multiplying each tem by, d d m k 0 (4) d d A slutin in the fm f the Maclauin seies (5) l a l leads t k l ( l ) (6) because cefficients highe than a l ae ze. The equatin (8) cntaining the aiable can nw be witten d R R d R dr k 0 (7) Page 4 f 7

5 When the alue f k in equatin (6) is substituted in equatin (7), btained is d R R d R dr l( l ) 0 (8) which pides d R R d R dr d l( l ) 0 (9) Multiplying each tem by R yields d R dr d l( l ) 0 R (0) and, afte extactin f fm the backet, leaes d R dr d R l ( l ) 0 () The electn spin is fund fm the seies epesentatin R a s () s which pduces an electn spin f [- ½]. T btain the the spin, we emply the seies R a s s (3) which pduces spin f [+ ½] Page 5 f 7

6 T btain inese enegy leels, which is t say belw-gundstate enegy leels, we ½ suppess the spin in equatin () by use f R a, which esults in d R dr ( ) d R ( l ½) 0 (4) F cicula bits in the subgund egin, the bital angula mmentum numbe l is ½, which endes the ttal angula mmentum l ½ equal t unity. Futhe, since the limiting alue f the phase elcity is the speed f light c, equatin (4) can nw be ewitten as d R dr d R c 0 (5) The ecipcal quantum enegy leels ae fund fm the seies epesentatin R a p p (6) Afte fist and secnd deiaties ae fund and placed in equatin (5), btained is p c 0 (7) which pduces (8) p c Page 6 f 7

7 whee p is the index f efactin ey nea the nucleus. The pincipal quantum numbe n is gien by n c 38 Thus the inese pincipal quantum numbes begin at n 6 The electn elcity at n is. 8 x 0 m/sec; at speed f light. and teminate at n. 37 n, the elcity is c, the 37 (9) CONCLUSION The standad wae equatin indicates that factinal quantum states exist. The slutin is squae integable, satisfying a fundamental tenet f quantum physics. Mills claim f 37 diffeent inese enegy leels seems cnfimed, as is Naudts elatiistic analysis shwing that at least ne inese quantum state in the hydgen atm exists. This helps us undestand the especially tight bnd f hydgen in metals, such as magnesium, which equies tempeatues in excess f 700K t elease the hydgen. 4 ACKNOWLEDGEMENTS The auth s inteest in inese quantum states was whetted by Pfess Rbet L. Call f West Viginia (90-997). It is in his memy that this pape is witten. REFERENCES: [] Naudts J. 005 On the hydin state f the elatiistic hydgen atm physics/ [] Rathke A. 005 A citical analysis f the hydin mdel New Junal f Physics 7 7 [3] Mills R. The Gand Unified They f Classical Quantum Mechanics [4] Stie W. et al. 005 Hydgen Stage in Magnesium Based Allys Pepint Pape-Am. Chem. Sc., Di. Fuel Chem. 50,, 5 Page 7 f 7