Kwizigqibo Dirac kaThixo. Dirac equation. theory endle Quantum

Eli nqaku igxininisa umsebenzi Paul Dirac alenxaki leyo safuma ubucukubhede quantum. Lichaza nezimaphambili ezingundoqo ezifunekayo ukuze baqonde intsingiselo ebonakalayo lenxaki, ngokunjalo iindlela isicelo sayo.

Science and izazinzulu

Umntu sinxulumana nenzululwazi, oko inkqubo yemveliso ulwazi zibe lwemilingo. Zenzululwazi, ngokoluvo abantu - it cranks abathetha ulwimi engaqhelekanga kunye abanekratshi kancinane. Ukubazi kunye umphandi, kude umntu zenzululwazi xa wayesithi yena akazange aqonde yemvelo esikolweni. Ngenxa yoko le ndoda endaweni yokubutha sibiyelwe ungabikho ulwazi lwenzululwazi, kunye nezicelo abafundileyo ngakumbi interlocutor ukuthetha lula kwaye ongenantandabuzo ngakumbi. Ngokuqinisekileyo Paul Dirac equation esixubusha, basamkela ngokunjalo.

amasuntswana asisiqalelo

Ubume mba lusoloko yitile iingqondo ukwazi. E Greece yamandulo, abantu baye baqaphela ukuba amanyathelo nezemarmore, owazeka kakhulu umlenze, imilo utshintsho ekuhambeni kwexesha, waza wacebisa: unyawo ngamnye okanye imbadada ihambisana enesuntswana mba. Ezi nkalo ziye zagqiba ukubiza "athom", oko kukuthi "ayahlukahlukenanga". Igama lihlala, kodwa kwenzeka ukuba athom kunye amasuntswana ezakha athom - umchiza enye, complex. Ezi amasuntswana kuthiwa sabaqalayo. Sinikezelwa umsebenzi equation Dirac leyo livunyelwe nje ukuchaza spin umsebenzi ovela, kodwa zibonisa ubukho antielectron.

Wave-yamasuntswana mbini

Ukuphuhliswa iifoto zobugcisa kwinkulungwane yeshumi elinesithoba kade, kuwandisa nje ukumila imprinting ngokwawo, ukutya kunye neekati, kodwa kwakhona kukhuthazwe amathuba yenzululwazi. Akuba ebuyile, ebamkele isixhobo imidlalo efana umfanekiso okhawulezayo (ukhumbule exposure ngaphambili kufikelelwe malunga 30-40 imizuzu), oososayensi baqalisa en endle ukulungisa ezahlukeneyo spectra.

ngelo xesha ingcamango ngesakhiwo kwezinto ezikhoyo ayikwazanga ukuchaza ngokucacileyo okanye ukuqikelela spectra kweemolekyuli ezintsonkothileyo. Okokuqala, lo yolingelo ka Rutherford wabonisa ukuba atom ayikho ayahlukahlukenanga njalo; yaba ingxenye enkulu entle kuyo inika electron lula ezimbi intliziyo yakhe. Ke kwafunyanwa radioactivity kwabonisa ukuba le kernel akukho litye lesikhumbuzo, kwaye wenziwa protons kunye neutron. Kwaye ngoko ke ukufunyanwa phantse ngaxeshanye umyinge wemali amandla, i Heisenberg ukungaqiniseki siseko kunye nohlobo probabilistic nezakhiwo amasuntswana yendawo ukunika amandla okuqhubela phambili kuphuhliso ngokunzulu indlela entsha zenzululwazi ekufundweni zehlabathi ezingqongileyo. A icandelo elitsha - nokwakheka amasuntswana asisiqalelo.

Umba ophambili ekuqaleni kwephakade eli lwezona enkulu yandile ultra-elincane ukuchaza ubukho inginginya yamasuntswana nezakhiwo kunye neempawu amaza.

Einstein wabonisa ukuba nkqu photon imperceptible inobunzima, njengoko into eqinileyo sifaka ukubetha kwentliziyo, leyo iwela (nesenzeko xi ukukhanya). Kulo mzekelo, amalinge amaninzi kwi ukusasazeka elektroni kwi nasezimfanteni bathi ubuncinane babe diffraction kunye uphazamiseko, oko abayinqobo kuphela ukuba itshangatshangiswe. Ngenxa yoko, kwafuneka avume: amasuntswana eziziziqalelo ngexesha elifanayo into esinobunzima kunye amaza. Oko kukuthi, ubunzima, bathi, ovela sanga "waluqaba" kwi package lwamandla ngokweempawu otshangatshangiswayo. Lo mgaqo lwamaza-yamasuntswana mbini eye wavumela ukuba uchaze kuqala kutheni electron engeyoyangeli ngumongo, yaye ngenxa yintoni zikhona izizathu ukujikeleza i-atom, kwaye zinakho kubo ngokukhawuleza. Ezi zinakho, usike spectrum ekhethekileyo nayiphi na into. Okulandelayo, iyevakala yamasuntswana physics kufuneka bachazelwe iimpawu amasuntswana ngokwabo, kwakunye benxibelelana.

Iliza umsebenzi amanani kwenani

Erwin Schrödinger wenza isimanga lusithe kwada kwaba lokuvula (ngokusekelwe kamva yakhe Pol Dirak wakha ingcamango yakhe). Ungqinile ukuba imeko nayiphi yamasuntswana samabanga aphantsi, umzekelo, ithetha electron wave umsebenzi ψ. Iyodwa, oko akuthethi akuthethi nto, kodwa oko kuya kowe amathuba okufumana i-electron kwindawo lithile isithuba. Kule miba amasuntswana nezakhiwo xa i-atom (okanye omnye system) luchazwa amanani amane quantum. Oku eziphambili (n), Orbital (l), iinkcukacha ngemagnethi (m) kunye spin (m _s) amanani. Ibonisa ngeempawu amasuntswana asisiqalelo. Njengoko isifaniso, uyakwazi wazise block ioli. iimpawu zayo - ubunzima, ubungakanani, umbala kunye nomxholo otyebileyo. Nakuba kunjalo, iimpawu ezichaza amasuntswana limalunga, lungenakuqondeka ungaziva, kufuneka bazazi kwinkcazo zemathematika. Umsebenzi Dirac nxaki ngu - ugxininiso kweli nqaku uzinikele yokugqibela, inani ukujikeleza.

spin

Ngaphambi kokuqhubeka ngqo lenxaki, kuyimfuneko ukuba achaze oko ibonisa spin inombolo m _s. Ibonisa eyakhe umfutho emboxo electron, kunye nezinye amasuntswana ezinesiqalelo. Eli nani usoloko eyakhayo kwaye bathathe ixabiso elipheleleyo, kwiqanda okanye ixabiso kwisiqingatha (ngokuba m _s = 1/2 electron). Spin - ubungakanani kumda wesangqa kwaye kuphela ukuba ichaza orientation electron. theory endle Quantum ibeka spin isiseko sentsebenziswano wotshintshiselwano, ayinazo savulwa e ubucukubhede enobuchwepheshe ngokubanzi. inombolo Spin ubonisa indlela kumda wesangqa kufuneka uvule ukuza yaso. Umzekelo bekuya kuba abaqhelekileyo ibhola-point ipeni (ukubhala inxalenye lizakuvumela kwicala ezintle kumda wesangqa). Ke wangena waya kwimeko yangaphambili, kuyimfuneko ukuba ukujika degrees 360. Le meko elivumelana emva 1. Xa kwisiqingatha umva, njengokujikeleza electron kufuneka degrees 720. Ngoko ke, ukongezelela intuition mathematical, kufuneka ziye ukucinga lwendawo ukuyiqonda le propati. Nje kusetyenzwa ngasentla kunye umsebenzi wave. Le yengundoqo i "zolinganiso" Schrodinger equation ngawo ichaza nesikhundla amasuntswana nezakhiwo. Kodwa lo ubudlelwane kwimo yalo yantlandlolo senzelwe amasuntswana spinless. Chaza imeko electron nga ukubamba kuphela xa gabalala le Schrödinger lenxaki, kwenziwa ethe kumsebenzi ka Dirac.

Bosons kunye fermions

ವಿನ್ಯಾಸ uyilo - amasuntswana kunye ixabiso ejikelezayo isiqingatha-elipheleleyo. Fermions zilungiselelwe kwiinkqubo (umz athom) ngokutsho uPauli exclusion Umgaqo: isekwimo ngalinye kufuneka kube ngaphezu kwesinye yamasuntswana. Ngenxa yoko, electron nganye kwi-atom yahluke kancinane zonke ezinye (ethile inani quantum linentsingiselo eyahlukileyo). theory intsimi Quantum uchaza elinye ityala - bosons. Zinelungelo spin, nabo bonke ngaxeshanye kule meko efanayo. Ukuphunyezwa kwale meko ekuthiwa bose-Einstein amafu. Nangona sekuthiwa kungqinwa kakuhle ithuba sethiyori nakukufumana oko, iya kusala oluqhutywa 1995 kuphela.

Dirac equation

Njengokuba besesitshilo ngasentla, Pol Dirak yayifumana inxaki zakudala electron entsimini. Kuchaza iwonga elinye fermions. Le ndlela yesitalato ubuhlobo entsonkothileyo yaye ezininzi, nangenxa ukwakheka kwalo kufuneka ibe ezininzi izigqibo ezibalulekileyo. Ifomu lenxaki imi ngolu hlobo lulandelayo:

- (mc ² α _{0 + c Σ k p k {} k = 0-3}) ψ (x, t) = i h {∂ ψ / ∂ t (x, t)},

apho m - ubunzima fermions (ingakumbi elektroni), c - uqina ukukhanya, p _k - abaqhubi ezintathu icandelo iyaqhubeka (nezamazembe x, y, z), H - zalungisa Planck kaThixo rhoqo, x kwaye t - zilungelelanise lomhlaba ezintathu (ehambelana nezamazembe X , Y, Z) kunye nexesha, ngokulandelelana, kunye ψ (x, t) - chetyrohkomponentnaya umsebenzi wave ezintsonkothileyo, α _{k (k} = 0, 1, 2, 3) - matrix uPauli. Le yokugqibela operator yomgama ukuba basebenze umsebenzi yomtshangatshangiso kunye nendawo yayo. Le ifomyula inzima kakhulu. Ukuze uqonde ubuncinane amacandelo yalo, kuyimfuneko ukuba baqonde iinkcazelo ezisisiseko ubucukubhede quantum. Kufuneka kwakhona babe nolwazi ephawulekayo zezibalo ubuncinane into eya kumda, matrix, kunye nomsebenzisi. uhlobo abaziingcali zale nxaki bathi ngaphezu kumacandelwana kwayo. A indoda ethile eyazi physics yenyukliya kunye ubucukubhede quantum uqhelene, baqonde ukubaluleka kulo mtshato. Nangona kunjalo, kufuneka uvume ukuba Dirac quadratic kunye Schrödinger - kuphela siseko eziziziqalelo inkcazo zezibalo yeenkqubo ezenzeka ehlabathini omyinge quantum. yemvelo yeengcingane, abaye bagqiba kwelokuba azinikele ukuze amasuntswana cebetshu benxibelelana, kufuneka ukuba ayiqonde kakuhle ezi nobuhlobo iqondo yokuqala neyesibini. Kodwa lo isayensi umdla, kwaye kule ndawo ungenza impumelelo okanye ziyaluthundeza igama lakhe, wabele ukuba inxaki, ukuguqulwa okanye impahla.

Intsingiselo ebonakalayo lenxaki

Njengoko uthembisile, sixelela into izigqibo uyayigubungela inxaki Dirac ukuba electron. Okokuqala, lo ngokunxulumene kucaca ukuba spin electron yi ½. Okwesibini, ngokutsho lenxaki, electron une ixesha analo ngemagnethi. Kuyinto elingana Bohr magneton (omnye umzuzu aphantsi magnetic). Kodwa ke ngenxa ezibalulekileyo kokufumana le ratio ilele kwi α yomqhubi _{k zokuqhubela.} Isiphelo le Dirac equation evela Schrödinger equation yathatha ixesha elide. Dirac ekuqaleni babecinga ukuba aba basebenzi abayithintelayo ubudlelwane. Ngoncedo lamaqhinga ezahlukeneyo zezibalo wazama ukuba zingabandakanywa lenxaki, kodwa akazange aphumelele. Ngenxa yoko, i equation Dirac for amasuntswana free iquka α umqhubi ezine. Ngamnye kubo imele matrix [4x4]. Ezimbini bahambelana ubunzima ezintle electron, nto leyo engqina ukuba kukho amagatya amabini ukujikeleza yayo. Abanye ababini unike isisombululo ukuba amasuntswana mass negative. Ulwazi nokungundoqo zemvelo zinika umntu ukugqiba ukuba akunakwenzeka ngokwenyani. Kodwa ngenxa yomzamo yafunyanwa ukuba matrices zimbini zokugqibela ukuba izisombululo amasuntswana ezikhoyo, electron malunga - anti-electron. Njengoko electron, i (ngoko wabiza le yamasuntswana) inobunzima, kodwa yoyalo positive.

i

Njengoko kaninzi kwenzeka Ixesha kwesayensi quantum Dirac ekuqaleni abazange bakholwe izigqibo zabo. Akazange abe nobuganga ukushicilela ngokuphandle kwingqikelelo ilungu elitsha. Nangona kunjalo, xa kukho inani lamaphepha kunye iisimpoziya kwi abaphengululi ezahlukeneyo ziye zigxininise ithuba ubukho bayo, nakubeni Aristotle. Kodwa kungekudala emva ukurhoxiswa kwesi ratio i idumileyo yabhaqwa radiation cosmic. Ngaloo ndlela, ubukho yayo iye yaqinisekisa empirically. I - ezifumanekayo abantu element lokuqala antimatter. I ozelwe njengoko isibini iwele (elinye iwele - yinto electron) kwi impefumlelwano photons kunye umphakathi kweziyobisi amandla aphezulu kakhulu kwintsimi womelele zombane. Nika amanani angeke (kwaye umfundi anomdla kufumana ngokwakhe zonke iinkcukacha eziyimfuneko). Nangona kunjalo, kubalulekile egxininisa ukuba lo isikali yesiqalo. Ukuba avelise ziluhlaza adingekayo kuphela udubulo supernova kunye kwezigaba esembindini. Kwakhona inani equlethwe eziba iinkwenkwezi ashushu, kuquka ilanga. Kodwa umntu usoloko welusa inzuzo yakhe. Ukutshatyalaliswa mba kunye antimatter unika amandla amaninzi. Ukunqanda le nkqubo kwaye wasibeka okulungileyo abantu (umzekelo, bekuya kuba iinjini ezisebenzayo leenqanawa oluphakathi ukuya ukutshatyalaliswa), abantu baye bafunda ukwenza protons elebhu.

Ngokukodwa, accelerators ezinkulu (ezifana LHC) ingadala isibini electron-i. Ngaphambili ke kuye kwacetyiswa ukuba kukho kuphela antiparticles ezinesiqalelo (ukongeza electron kubo ezimbalwa ngaphezulu) yonke antimatter, kodwa. Nokuba intwana encinane na crystal of antimatter kwakuza amandla umhlaba (mhlawumbi Interface Superman waba antimatter?).

Kodwa yeha, ukudalwa eziba antimatter inzima ngaphezu hydrogen angabhalwanga zibhalwe endaweni yonke. Noko ke, xa umfundi ecinga ukuba impefumlelwano umba (qaphela, oko ke into, kungekhona electron omnye) kunye i ukutshatyalaliswa kwangoko iphela, yena bayaphazama. Xa deceleration i ngesantya esiphezulu kwezinye ulwelo ne non-zero amathuba kuvela isibini electron-i ezinxulumene, ebizwa positronium. Le ukubunjwa has ezinye iimpawu atom nkqu ukukwazi ukungena ekudibaneni kwemichiza. Kodwa kukho eli ibhayisekili elifutshane ixesha ethe uze nangoku etshabalalisa kunye yazingcolisa amabini, kwaye kwezinye iimeko, kunye gamma ezintathu.

ezingalunganga lenxaki

Nangona ukuba olu lwalamano yafunyanwa ngama anti-electron kunye antimatter, isiphathele ethile ebalulekileyo. Ukubhala zibalo kunye nomzekelo wakha isekelwe phezu kwayo, aninako ukuqikelela amasuntswana bezalwa batshatyalaliswa ngayo. Oku isigqebelo yinqobo yehlabathi quantum: ithiyori, kwangaphambili ukuzalwa ngababini nto-antimatter, nako ukuchaza ngokwaneleyo kule nkqubo. Esi sithintelo sele ziphelisiwe theory entsimini quantum. Ngokubonisa quantization kwamabala, le modeli uchaza ngokuzibandakanya kwabo, kuquka ukwakhiwa kunye ukutshatyalaliswa kwamasuntswana nezakhiwo. Xa "theory intsimi quantum" kule meko ithetha kota ethile kakhulu. Le yinkalo ophanda ukuba lifunda ukuziphatha kwamasimi quantum.

equation Dirac xa ezihambelanayo zezindlu

Okokuqala, makhe uyazi ukuba yintoni zezindlu nokulawula inkqubo. Endaweni yesiqhelo asi ezintathu macala nkqo ukuba ukujonga indawo ngqo yencopho isithuba usebenzisa ekujikeni, embindini kunye nokuphakama. Oku kuyafana njenge nokulungelelanisa inkqubo polar-moya, kodwa wongezelela njengomlinganiso sesithathu - ukuphakama. Le nkqubo luncedo xa ufuna ukuchaza okanye ukuphanda umphezulu macala malunga umgca enye. ubucukubhede Quantum sisixhobo esiluncedo kakhulu kwaye aluncedo ukuba unga nciphisa ngokubaluleka ubungakanani inani neefomula kunye izibalo. Oku ngenxa wolingano yezihlunu electron efini i-atom. I Dirac equation iyatyhilwa kwi zilungelelanise zezindlu ngokwahlukileyo kancinci ngaphezu kwesiqhelo kwinkqubo, yaye ngamanye amaxesha ikhupha iziphumo ezingalindelekanga. Ngokomzekelo, ezinye izicelo ingxaki yokumisela ukuziphatha amasuntswana nezakhiwo (idla electron) kwi quantized ukuguqula uhlobo lwefildi zibalo sele ezihambelanayo zezindlu.

Ukusebenzisa zibalo ukujonga isakhiwo kwamaqondo eparticulate

Le equation ichaza amasuntswana eziziziqalelo: abo musa zibandakanya izinto kakhulu. Iinzululwazi zale mihla uyakwazi ukulinganisa amathuba otsalayo ngokuchanileyo eliphezulu. Ngenxa yoko, nonokungangqinelani ukubala usebenzisa Dirac amaxabiso equation ngokomfuniselo kulinganiswa mzuzu magnetic iya kubonisa ngqo isakhiwo entsonkothileyo amasuntswana. Khumbula, lenxaki usebenza fermions, abo basonta isiqingatha-elipheleleyo. Isakhiwo elinzima protons kunye neutron siqinisekiswe ngokusebenzisa le nxaki. Ngamnye kubo iqulathe amacandelo kakhulu ekuthiwa quarks. Gluon endle ephethe quarks kunye, ngokungavumeli uqhawuke. Kukho ingcamango yokuba quarks - akukho nto amasuntswana kakhulu ayelandela ihlabathi lethu. Kodwa logama nje abantu abanayo kobuchwepheshe ngokwaneleyo ukuqinisekisa oku.