[Algadir*, 5(2): February, 2016] ISSN: (I2OR), Publication Impact Factor: 3.785

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1 [Algadr*, 5(): February, 6] ISSN: (IOR), Publatn Impat Fatr: IJSRT INTRNATIONAL JOURNAL OF NGINRING SCINCS & RSARCH TCHNOLOGY SCHRÖDINGR QUANTUM QUATION FROM CLASSICAL AND QUANTUM HARMONIC OSCILLATOR Lutf Mhammed AbdAlgadr*, Mubarak Drar Abdallah, Amel AbdAllah, Rawa.AA.Algan, Sawsan Ahmed lhur Ahmed Hurymlla Cllege f Sene & Humanty Studes, Shaqra Unversty-KSA. Internatnal Unversty f Afra- Cllege f Sene-Department f Physs & Sudan Unversty f Sene & Tehnlgy-Cllege f Sene-Department f Physs Khartum-Sudan. Sudan Unversty f Sene & Tehnlgy-Cllege f Sene-Department f Physs Khartum-Sudan. Sudan Unversty f Sene & Tehnlgy-Cllege f Sene-Department f Physs Khartum-Sudan. Unversty f Bahr-Cllege f Appled & Industral Senes-Department f Physs Khartum Sudan. ABSTRACT A new quantum mdel that aunts fr the medum frtn s derved. The frst advantage s the addtn f natural sllatn f partle. The send advantage s the nrpratn f fratn effet n the Hamltnan peratr. Ths means that bth Shrödnger equatn and energy gen equatn are affeted by frtn. The gen energy s nt affeted by frtn, whh s n dret nflt wth experment and mmn sense. INTRODUCTION Quantum Frtnal Osllatng and Bltzmann Dsruptn Law The desrptn f partles and waves mvng nsde a resstve medum fr quantum systems plays mprtant rle n superndutvty and super fluds, as well as nan system [,,3]. The theretal mdels that are develped t desrbe quantum frtn; the quantum treatment f ths prblem s based n satterng llsn theres whh are very mplex. Thus ne needs new quantum apprah that van smply takles frtn effets f the medum, Dfferent attempts wave made t nstrut suh mdel the mst prmsng are n that based n relaxatn. In ths mdel the slutns f quantum equatn lead t radatve deay law and transprt prbablty. Thus ne need a well-defned framewrk perfrms ths task. Ths an be dne, n ths hapter by utlzng Maxwell's equatn and plasma equatns. The tme attenuatn effent frm Maxwell's equatn Maxwell's thery s ne many theres that an desrbe eletrmagnet feld. The equatn f the eletr feld ntensty nsde a plarzed medum feld, Takes the frm [see equatn (-3--8)]: P. t t t The slutn f ths equatn an be expressed n terms f tme attenuatn effent, wave number K, and angular frequeny, t be n the frm [4] t t e e kx (.) The dsplaements f harges an be desrbed by: t kxt e e X (.3) The eletr dple mment an thus defne n terms f harge densty: t /( Kx t ) t ne X e n X e n X e e e e ()Dfferentatng (.) wth respet t X and t yelds:.4 http: // Internatnal Jurnal f ngneerng Senes & Researh Tehnlgy [67]

2 [Algadr*, 5(): February, 6] ISSN: (IOR), Publatn Impat Fatr: K, K x x,.5 t t () Dfferentatng (.) wth respet t t gves: P x x x e n e n x ele t e n x e n x ele ele Insertng equatns (.5), (.6) n equatn (.) yeld: e n x K e n K x.7 Thus equatn (.7) reads: e n x P K t e n x K.6 But sne the speed f lght s gven by: Thus equatn (.7) reads e n x P K t e n x K.8 But: f K f http: // Internatnal Jurnal f ngneerng Senes & Researh Tehnlgy [68]

3 [Algadr*, 5(): February, 6] ISSN: (IOR), Publatn Impat Fatr: Thus: e n e x quatn real parts n bth sdes n (.9) e ne x Sne the speed f lght s gven large Hene:. Thus the absrptn effent s gven by: e n x ele.. xpressn () an be smplfed by usng the ndutvty expressn fr dret urrent: ne m And by usng the eletrn equatn under the atn f eletrmagnet feld, where: Thus: m x x e e e x e t n x e m.4 Thus a dret substtutn f (.3) and (.4) n (.) yelds: e n m e n e m.5 One an als engrge plarzatn term n the equatn (a) t get:.6 Sne fr sulatng eletrn the equatn f mtn s: mv e t m x x e t e e t n.7 v dx / d t x.8 Sne Hene: Usng the relatn: mv e.9.9 (.3) http: // Internatnal Jurnal f ngneerng Senes & Researh Tehnlgy [69]

4 [Algadr*, 5(): February, 6] ISSN: (IOR), Publatn Impat Fatr: ne J n ev. m Therefre: n e T ne m m T,. Insertng the mplex ndutvty f () n equatn (6) yelds: quatng magnary parts ne gets:..3 Usng C s very large, ne an neglet the frst term n the braket,.e: T get:.4.5 In vew f n equatn (.4).The absrptn effent (.5) s gven by: ABSORPTION COFFICINT AND RLAXATION TIM FOR POLARIZD AND NON POLARIZD MATRIAL:.6 Cnsder an eletrn sulatng naturally wth frequeny w and affeted by the sulatng eletr feld[5,6]: The equatn f mtn fr suh eletrn s gven by: d v m kx e dt Where: mv 3. e t K m X x e t V x There fr equatn ( ) bemes: 3.3 m v m v m v m x e m v e m v e http: // Internatnal Jurnal f ngneerng Senes & Researh Tehnlgy [7]

5 [Algadr*, 5(): February, 6] ISSN: (IOR), Publatn Impat Fatr: By settng: Thus: V 3.5 e e m m Ardng t the relatn between urrent densty, velty and ndutvty ne gets: n e J n ev 3.7 m Hene the ndutvty s gven by: n e m Fr nn-plarzed medum, equatn (.) an be slved by assumng: k x t e T get: K In vew f ths equatn besde (3.8) ne gets: K C ne m (3.9) If the wave length n the medum s near t that f free spae t fllws that: K f f C (3.) As a result: K C (3.) Hene usng equatn (3.) n equatn (3.9) yelds: http: // Internatnal Jurnal f ngneerng Senes & Researh Tehnlgy [7]

6 [Algadr*, 5(): February, 6] ISSN: (IOR), Publatn Impat Fatr: (3.) A smlar result an be fund fr plarzed materal Ardng t equatn (.3): X x e t X v x e t V e t X v P e n x 3.3 Thus: P e n x n ev J t Thus equatn (.8) fr negleted bemes: K C Ths s typal equatn (3.9) thus gves agan: (3.4) Ardng t plank hypthess the rgnal energy and the energy fr frtnal medum are gven by: f (3.5) Ths expressn fr frtnal energy agrees wth eqn (.6) and (.) QUANTUM QUATION FOR FRICTIONAL MDIUM In vew f equatn (.) n a resstve medum wth the ad f eqn (.) ne an wrte the wave funtn smlar t. Ths s justfable as far as[7,8] Number f phtn Number f partles Thus, ne an wrte t be: A e t t t 4. t Hˆ 4.3 Thus the energy peratr takes the frm: H ˆ 4.4 Usng: 4. http: // Internatnal Jurnal f ngneerng Senes & Researh Tehnlgy [7]

7 [Algadr*, 5(): February, 6] ISSN: (IOR), Publatn Impat Fatr: P V (4.5) m P V (4.6) m p x p x In 3 dmensns: p (4.7) V t m V t m 4.8 STRING OSCILLATORY SOLUTION T fnd slutn fr harmn sllatr, t s mprtant t separate varables. Thus ne an wrte the wave funtn[9] r, t f t u r 5. Insertng f equatn (5.) n (4.8) yelds: f ft Therefre: u V mu f f t The slutn f ths equatn s: t f A e Substtutng (5.4) n (5.3) yelds: (5.) Fr Harmn Osllatr the ptental s gven by: V k x Ths equatn (5.) redues t: 5.6 u k x u u u m But the energy f harmn Osllatr s gven by: n http: // Internatnal Jurnal f ngneerng Senes & Researh Tehnlgy [73]

8 [Algadr*, 5(): February, 6] ISSN: (IOR), Publatn Impat Fatr: n,,3,... The harmn Osllatr satsfes perdty ndtn,.e: f t T f t 5.9 In vew f equatn (5.4) ths requres: T e s T s n T Ths means that: s T sn T Hene: T s S,,3,... s s T 5. Insertng (5.) n (5.5), the energy s gven by: s 5. Ths energy lst by frtn s thus gves ardng t eqn (5.8) and (5.) gven by: n s 5. f DISCUSSION Maxwell equatn fr eletr feld s used t fnd a useful expressn fr absrptn effent was fund. The slutn suggested nludes dampng term. The relatn between plarzatn and dsplaement, tgether wth the expressn f ndutvty fr dret urrent, n addtn t the eqn f eletrn mtn n the presene f eletr feld and frtns, are all used t fnd. It s fund als that s equal t the repral f relaxatn tme. Usng the eletrn equatn f mtn, tgether wth ndutvty relatn f alternatng urrent, besde Maxwell equatn slutn fr travellng an attenuated wave n setn(3) a useful expressn fr absrptn effent s fund als. Ardng t eqn(3.6) velty relatn s fund and s nserted n eqn(3.7)t fnd mplex ndutvty n eqn(3.8). Ths eqn s substtuted n Maxwell slutn n eqn (3.9). By assumng the wave number K t be equal t that f free spae a useful expressn fr frtn energy eqn (3.5) s fund by usng Plank quantum hypthess, fr nnplarzed and plarzed medum. It s very strkng t nte that ths frtnal energy expressn s smlar t that f eqn (4.).Quantum quatn fr frtnal medum, whh s redued t rdnary shdngereqn s fund n setn 4 eqn (4.8).By treatng partles as vbratng strngs r mvng n a rular rbt, a useful expressn f frtn energy s fund. The frtn energy s shwn t be quantzed. CONCLUSION Maxwell quatns fr dampng r nn-dampng eletrmagnet wave, n the presene f frtn an be used t derve new Shrdnger quatn; ths equatn redues t rdnary Shrdnger quatn and shws quantzed frtn energy. RFRNCS [] Pdern M., Przyvnk, S., Stalnsk B., Phys. State Sl., 4, K73 (). [] Martn A. Green, Slar ell-internatnal Cmpany, Irag, 3 Page [3] C.Dam-Hansen P.M Jhansen, P.M.Petersen, V.M. Frdkn- Influene f and externally appled magnet feld n Vtra nteratn n LNbO3: Fe rystals, B5, R398-R3 () [4] S.Weble, A. Sparenber, G.L.J.A.Rekken, D.Laste, and B.A.Van Tggelen, Phtn Hall effet n absrbng meda, 6, (4) http: // Internatnal Jurnal f ngneerng Senes & Researh Tehnlgy [74]

9 [Algadr*, 5(): February, 6] ISSN: (IOR), Publatn Impat Fatr: [5] T.M.Perkarek, B.C.Crker, Mtkwsk and A.K.Ramdas, Magnet measurement n the III-VI dluted magnet semutr Ga-xMnxSe Vlume 83, Issue, pp (3) [6] Hesenberg, Werner (). In Rehenberg, Helmut. Deutshe und Jüdshe Physk. Pper. ISBN [7] Jurnals-Phys. RevB, Vlume 38, Issue -Funtnal ntegral theres f lw dmensnal quantum Hesenber-3. [8] L.I. Shff, Quantum Mehans (M Graw Hll, Tky, 5) [9] Ludv, Anna (). ffett Hesenberg. La rvluzne sentfa he ha ambat la stra. Rma: Armand. p. 4. ISBN http: // Internatnal Jurnal f ngneerng Senes & Researh Tehnlgy [75]