Iziphetho Dirac sika. Dirac equation. Quantum ensimini theory

Lesi sihloko sigxile kakhulu umsebenzi uPawulu Dirac kwesibalo okuyinto ahlanganiswe kakhulu quantum Mechanics. Lichaza nemiqondo eyisisekelo kudingekile ukuba siqonde incazelo ezingokomzimba equation, kanye nezindlela kwesicelo yayo.

Isayensi ososayensi

Umuntu ongakaphathelani isayensi, kuba khona ulwazi yenqubo ukukhiqizwa umphumela ezinye imilingo. Ososayensi, ngokubona abantu - ke cranks abakhuluma ulimi angalwazi futhi kancane ezikhukhumezayo. Ukuqalisa bajwayelane umcwaningi, neze nesayensi muntu obekade wathi babengakuqondi physics esikoleni. Ngakho umuntu emgwaqweni ibiyelwe ngiwunqume ulwazi lwesayensi, futhi ezinye izicelo abafundile interlocutor ukukhuluma kulula futhi enembile. Ngokuqinisekile uPawulu Dirac kwesibalo izincwadi esizifundayo, wamukela kanye.

izinhlayiya aphansi

Isakhiwo ndaba njalo yavusa izingqondo nelukuluku. EGrisi lasendulo, abantu baye baqaphela ukuthi ngezitebhisi ezenziwe ngemabula, okuyinto Kwangithatha umlenze, ushintsho ukuma ngokuhamba kwesikhathi, futhi wasikisela: onyaweni noma wembadada ihambisana kancane encane ndaba. Lezi zici sinqume ukubiza "ama-athomu", okungukuthi "indivisible". Igama uhlala, kodwa kwathi kwama-athomu nezinhlayiyana izinhlayiya ezakha ama-athomu - enkompolo esifanayo, eziyinkimbinkimbi. Lezi zinhlayiya abizwa ngokuthi aphansi. It lunikezelwe umsebenzi bona Dirac kwesibalo okwamvumela hhayi kuphela ukuchaza spin i-electron, kodwa futhi kusikisele khona antielectron.

Wave-kuyizinhlayiyana webumbacambili

Ukuthuthukiswa ubuchwepheshe izithombe ngasekupheleni kwekhulu nesishiyagalolunye, kuhilelani hhayi kuphela fashion imprinting ngokwayo, ukudla namakati, kodwa futhi amathuba isayensi. Njengoba base bethole ithuluzi Ukugunda ezifana isithombe esheshayo (khumbula ngaphambili ukuchayeka safinyelela imizuzu mayelana 30-40), ososayensi baqala ngobuningi ukulungisa ezihlukahlukene spectra.

Ekhona ngaleso theory sikhathi isakhiwo izinto akakwazanga ukuchaza ngokucacile noma zibikezela spectra ka yezinhlayiya eziyinkimbinkimbi. Okokuqala, ukuhlola odumile uRutherford wabonisa ukuthi i-athomu akuyona indivisible ngakho; inhliziyo yakhe yaba nzima nucleus omuhle emhlabeni alinikela electron lula ezimbi. Khona-ke kokutholakala radioactivity wafakazela ukuthi ikhenela akuyona dwala, futhi yakhiwa proton kanye neutrons. Bese kuthi-ke ukutholakala cishe ngesikhathi esisodwa quantum energy, lo Heisenberg ukungaqiniseki isimiso nemvelo probabilistic aphansi izinhlayiya indawo bafake umfutho ekuthuthukiseni a indlela ngokuyinhloko entsha yesayensi ekutadisheni izwe elizungezile. A new kwesigaba - physics izinhlayiya aphansi.

Inkinga enkulu ekuqaleni engu yezinto ezinkulu e isikali ultra-ezincane kwaba ukuchaza khona aphansi kuyizinhlayiyana uquqaba futhi igagasi izakhiwo.

Einstein wafakazela ukuthi ngisho i-albhamu yezithombe imperceptible inobungako, njengoba okuqinile okuhambisa ishayela, oluba (ukukhanya ingcindezi mkhuba). Kulokhu, ucwaningo eminingi kusakazeka electron emifantwini ka wathi okungenani banabo umumo womsebenzi nokugxambukela, kuba eyinqaba kuphela ngiyontengantenga. Ngenxa yalokho, kwadingeka ngivume: izinhlayiya aphansi ngesikhathi esifanayo into ngongqimba futhi kwakuza igagasi. Okungukuthi, nenqwaba, uthi, i-electron kungathi "ezigcotshwe" energy iphakheji sezindawo wave. Lomgomo of igagasi-kuyizinhlayiyana webumbacambili ukuvumele ukuchaza kuqala kunazo zonke esenza electron ongawi nucleus, futhi kungaziphi izizathu ezikhona emzileni athomu, futhi ukuguquka phakathi kwabo kukhona ngokuzumayo. Lezi ukuhwebelana futhi zikhiphe spectrum ahlukile iyiphi into. Ngokulandelayo, aphansi kuyizinhlayiyana physics kumele uchaze kwaba izindawo izinhlayiya ngokwabo, kanye nokusebenzisana yabo.

Umsebenzi igagasi le quantum izinombolo

Erwin Schrödinger wenza kumangaza futhi kuze kube yileso usithe kuvulwa (ngesisekelo wakhe kamuva Pol Dirak eyakhelwe bayihlaba kakhulu inkolelo yakhe). Akabanga ukuthi isimo noma iyiphi kuyizinhlayiyana aphansi, isibonelo, uchaza i-electron wave umsebenzi ψ. Ngu uqobo, akusho lutho, kodwa ngeke Square Amathuba okuthola electron weyesi inikezwe isikhala. Kuleli zinga izinhlayiya aphansi e-athomu (noma kwenye ohlelweni) ochazwa izinombolo ezine quantum. Lokhu main (n), esemkhathini (l), i-magnetic (m) kanye spin (m _s) izinombolo. Zibonisa sezindawo izinhlayiya aphansi. Njengoba isifaniso, ungaletha block uwoyela. izici zayo - isisindo, isayizi, umbala kanye nokuqukethwe amafutha. Nokho, izindawo ezichaza izinhlayiya aphansi, ayikwazi waqonda intuitively, kufanele baqaphe ngokusebenzisa incazelo zezibalo. Umsebenzi Dirac ndaba kuyindlela - focus kwalesi sihloko Sizokwenza yokugcina, inani spin.

spin

Ngaphambi kokuqhubeka ngqo equation, kubalulekile ukuchaza ukuthi isho _s inombolo spin _m. Ibonisa siqu umfutho emincane electron, nezinye izinhlayiya aphansi. Le nombolo eyakhayo ngaso sonke isikhathi futhi kungase kuthathe inani inamba, kuqanda ukubaluleka isigamu (i m _s = 1/2 electron). Spin - usayizi Vector futhi nguye kuphela esichaza ukuma electron. Quantum ensimini theory ubeka spin ngesisekelo ukuxhumana exchange, esingeyena uzakwabo e Mechanics ngokuvamile enembile. inombolo Spin kubonisa ukuthi vector kumelwe ujike ukuza esimweni saso sokuqala. Isibonelo kungaba ezejwayelekile ibhola-iphuzu ipeni (ukubhala ingxenye kuzovumela uhlelo isiqondiso esiqondile vector). Lokho weza isimo sokuqala, kubalulekile ukuze ujike 360. Lesi simo sifana ngemuva 1. Lapho ingxenye emuva, njengoba ukujikeleza electron kumele kube 720 degrees. Ngakho, ngaphezu umuzwa zezibalo, kumele baye basungula ukucabanga lwezendawo ukuthi uyayiqonda le impahla. Vele ngenhla asebenzelana ngayo umsebenzi wave. Kuyinto main "umlingisi" Schrödinger kwesibalo ngu echaza isimo nesikhundla izinhlayiya aphansi. Kodwa lobu buhlobo injalo yasekuqaleni senzelwe izinhlayiya spinless. Chaza isimo electron ungakwazi kuphela ubamba uma nje okungaqondile we Schrödinger equation, osekwenziwe emsebenzini Dirac.

Bosons futhi fermions

Fermion - izinhlayiya nge uhhafu-inamba spin value. Fermions ahlelwe izinhlelo (isb ama-athomu) ngokuvumelana Pauli inyumbazane isimiso: esimweni ngasinye kufanele kube khona abangaphezu koyedwa nezinhlayiya. Ngakho, ama-electron ngamunye nakuyi-athomu Kuthi sihluke bonke abanye (inombolo ethile quantum linencazelo ezahlukene). Quantum ensimini theory uchaza esinye icala - bosons. Banezinhliziyo spin, futhi zonke kungaba kanyekanye ibe isimo esifanayo. Ukuqala kokusetshenziswa Kulokhu ngokuthi Bose-Einstein ukufingqa. Naphezu sasivumela waqinisekisa kahle kungenzeka theory ukuze uthole it, ngokuyinhloko eyenziwa ngo-1995 kuphela.

Dirac kwesibalo

Njengoba sishilo ngenhla, Pol Dirak etholakala i equation of classical ensimini electron. Iphinde lichaza isimo nezinye fermions. Inzwa ezingokomzimba ubuhlobo liyinkimbinkimbi futhi enezici, futhi ngenxa ezakheke kufanele kube eningi iziphetho ayisisekelo. Ifomu le-equation simiswe ngalendlela lelandzelako:

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

lapho m - mass fermions (ikakhulukazi electron), c - Isivinini yokukhanya, p _k - opharetha ezintathu umfutho ingxenye (the izimbazo x, y, z), h - okuqoqiwe Planck sika njalo, x futhi t - izixhumanisi ezintathu ngekwendzawo (elihambisana izimbazo X , Y, Z) kanye nesikhathi, ngokulandelana, futhi ψ (x, t) - chetyrohkomponentnaya wave eziyinkimbinkimbi umsebenzi, α _{k (k} = 0, 1, 2, 3) --matrix Pauli. I yamuva ayizona opharetha komugqa ukuthi isinyathelo umsebenzi wave futhi isikhala salo. Lokhu Ifomula kubenzima. Ukuze uqonde okungenani izingxenye zalo, kubalulekile ukuqonda izincazelo eziyisisekelo quantum Mechanics. Kufanele ifa ulwazi emangalisayo zezibalo okungenani ukwazi ukuthi vector,-matrix, futhi opharetha. ifomu Specialist of the equation ukusho baningi ngisho nangaphezu kwezinwele izingxenye zalo. A umuntu owayeyisazi wesayensi yenuzi kanye quantum Mechanics ujwayelene, ukuqonda ukubaluleka kwalesi ubuhlobo. Nokho, kumelwe sivume ukuthi Dirac equation kanye Schrödinger - kuphela izimiso zokucathula incazelo nezibalo izinqubo ezenzeka emhlabeni kwenani kobukhulu. zesayensi theory, abaye yanquma azinikele izinhlayiya aphansi ekuhlanganyeleni kwabo, kufanele baqonde okushiwo la ubudlelwane ngezinga lokuqala nelesibili. Kodwa lokhu isayensi kuyathakazelisa, futhi kungalesi sikhathi lapho endaweni ungenza ukuphumelela noma ukuvuselela igama lakhe, ukwaba ku-equation, ukuguqulwa noma impahla.

Okwakushiwo ezingokomzimba kwesibalo

Njengoba sathembisa, sitshela yiziphi iziphetho uyazifihla Dirac equation for electron. Okokuqala, lokhu kuqhathaniswa kuyacaca ukuthi spin electron kuyinto ½. Okwesibili, ngokuvumelana equation, electron ine isikhashana eziwumgogodla kazibuthe. Kuyinto ilingane Bohr magneton (owodwa nje aphansi kazibuthe). Kodwa umphumela ebaluleke kakhulu yokuthola lolu isilinganiso itholakala ukucasha opharetha α _k. Isiphelo Sesimiso Dirac kwesibalo kusukela Schrödinger kwesibalo wathatha isikhathi eside. Dirac ekuqaleni wayecabanga ukuthi laba basebenzi kuphazamise ubuhlobo. Ngosizo namasu ehlukene zezibalo wazama ukubekela eceleni kwabo kusukela equation, kodwa akazange aphumelele ukubuyisana nomkakhe. Ngenxa yalokho, i-Dirac equation for izinhlayiya khulula kuhlanganisa opharetha α ezine. Ngamunye wabo limelela matrix [4x4]. Amabili sihambisana mass omuhle i-electron, okuyinto efakazela ukuthi kunezinhlobo ezimbili zoMthetho wokuPhathwa spin yayo. Abanye ababili ukunikeza isixazululo mass negative izinhlayiya. Ulwazi kakhulu eziyisisekelo physics ukunikeza umuntu baphethe ngokuthi kuyinto engenakwenzeka empeleni. Kodwa ngenxa ukuhlola kwatholakala ukuthi ezimbili zokugcina matrices kukhona izixazululo izinhlayiya ekhona, electron okuphambene - anti-electron. Njengoba ama-electron, positron (ngakho wabiza lo kuyizinhlayiyana) inobungako, kodwa lokushaja omuhle.

positron

Njengoba ngokuvamile kwenzeka ngenkathi nalokho okutholwe quantum Dirac ekuqaleni abazange bakholwe eziphethweni zayo. Akazange alinge obala ukushicilela isibikezelo nezinhlayiya entsha. Nokho, eziningi amaphepha symposia ku izazi ezihlukahlukene ziye zagcizelela ukuthi kungenzeka ukhona, nakuba hhayi ongoti kwezempilo abathi zihlobene. Kodwa ngokushesha ngemva ukuhoxiswa lokhu isilinganiso positron abadumile latholakala cosmic ngemisebe. Ngakho, le ndawo yayikhona iye yaqinisekisa empirically. Positron - the ezitholakala kubantu isici sokuqala antimatter. Positron azalwe njengomuntu eyodwa pair twin (elinye iwele - kuyinto electron) e nokuxhumana izinhlayiyana eziningi zokukhanya nge eliphezulu kakhulu amandla izidakamizwa cores ensimini eqinile kagesi. Nika izibalo thina ngeke (kanye umfundi nesithakazelo uzothola yena lonke ulwazi olufanele). Nokho, kuwufanele egcizelela ukuthi lokhu ngesilinganiso cosmic. Ukukhiqiza edingekayo amandla izinhlayiyana eziningi zokukhanya ungakwazi kuphela supernova ukuqhuma ukushayisana Galactic. kunjalo futhi e inombolo eziqukethwe nuclei zezinkanyezi ashisayo, kuhlanganise ilanga. Kodwa umuntu njalo ivame ukuze izinto zimhambele kahle. Ukubhujiswa ndaba futhi antimatter unika amandla amaningi. Ukunqanda le nqubo futhi uwubeke ukuzuzisa abantu (isibonelo, kungaba izinjini ngempumelelo imikhumbi interstellar ukuba yokubhujiswa), abantu baye bafunda ukwenza proton egunjini lokucwaninga esibhedlela.

Ikakhulukazi, accelerators ezinkulu (njenge LHC) ungakha electron-positron pair. Ngaphambili futhi kuye kwasikiselwa ukuthi kukhona antiparticles aphansi hhayi kuphela (ngaphezu electron kubo ambalwa ngaphezulu), kodwa wonke antimatter. Ngisho obuncane iyiphi crystal of antimatter uzonikeza amandla iplanethi (mhlawumbe Kryptonite Superman kwaba antimatter?).

Kodwa-ke ngeshwa, ukudalwa antimatter nuclei ngoyisiwula kusinda kunakho hydrogen ayizange atloliwe yonke. Nokho, uma umfundi acabanga ukuthi nokuxhumana ndaba (uqaphele, kungukuqiniseka, esingesona electron eyodwa) nge positron yokubhujiswa ngokushesha kuyaphela, nguye iphutha. Lapho deceleration positron ngesivinini kwezinye uketshezi nge-non-zero okungenzeka kuphakama ahlobene electron-positron pair, ngokuthi positronium. Lokhu kumiswa has ezinye izindawo athomu ngisho nekhono ungene zamakhemikhali. Kodwa kukhona lokhu ethambile Ngohlelo isikhathi esifushane bese namanje bhubhisa nge ekushayweni ezimbili, futhi kwezinye izimo, futhi abathathu gamma rays.

nemibi ezothando

Naphezu kweqiniso lokuthi ngokusebenzisa le ubuhlobo kwatholakala anti-electron futhi antimatter, it has a ethile ebalulekile. Ukubhala ngezibalo imodeli eyakhelwe kwezindlu kusekelwe kuyo, abakwazi ukubikezela ukuthi izinhlayiya bezalwa futhi ubhujiswe. Lena indida engavamile emhlabeni quantum: imfundiso yokuziphendukela, wabikezela ukuzalwa ngazimbili ndaba-antimatter, akakwazi ngokwanele ukuchaza le nqubo. Lokhu kusimo sekuqediwe e quantum ensimini theory. Ngokwethula quantization emasimini, lokhu imodeli uchaza ekusebenzelaneni kwabo, ehlanganisa indalo futhi ukubhujiswa izinhlayiya aphansi. Ngu "quantum ensimini umbono" Kulokhu kusho igama elicacile kakhulu. Lena indawo physics ukuthi etadisha ukuziphatha Amasimu quantum.

kwesibalo Dirac e-izixhumanisi cylindrical

Ukuze uqale, ukukwazisa ukuthi cylindrical Ukudidiyela uhlelo. Esikhundleni evamile ezintathu izimbazo Okusizayo perpendicular ukucacisa indawo esiqondile iphuzu emkhathini usebenzisa i-engeli, engaba futhi ukuphakama. Lokhu kuyafana a polar Ukudidiyela uhlelo indiza, kodwa kwenezele esinye isici sesithathu - ukuphakama. Lolu hlelo kuyasiza uma ufuna ukuchaza noma ukuphenya surface ziyalingana mayelana eyodwa axis. quantum Mechanics iyithuluzi eliwusizo kakhulu futhi Ukugunda ezingaba kakhulu ukunqinda inani amafomula izibalo. Lo is phetho of wesimethri Axial fu electron e-athomu. I Dirac kwesibalo isixazululekile e izixhumanisi cylindrical kancane ehlukile kokujwayelekile ohlelweni, futhi ngezinye izikhathi kuba nemiphumela engalindelekile. Ngokwesibonelo, ezinye izinhlelo zokusebenza inkinga yokunquma ukuziphatha izinhlayiya aphansi (ngokuvamile electron) ku quantized uguqule uhlobo lomkhakha zibalo ixazululwe ukuze izixhumanisi cylindrical.

Ukusebenzisa zibalo ukunquma nokwakheka particulate

Lokhu kwesibalo uchaza izinhlayiya aphansi: labo abangahambi aqukethe izakhi ngisho ezincane. Isayensi yanamuhla uyakwazi ukukala izikhathi kazibuthe ngokunemba high. Ngakho, ukungafani ukubala besebenzisa Dirac kwesibalo amagugu Ucwaningo kulinganiswa okwamanje la mandla kazibuthe ngeke ngokungaqondile ukhombise isakhiwo eziyinkimbinkimbi izinhlayiya. Khumbula, lokhu kwesibalo osebenza ku fermions, nengxenye-inamba yabo spin. eyinkimbinkimbi of proton kanye neutrons kwaqinisekiswa ngokusebenzisa le equation. Ngamunye wabo siqukethe izingxenye ngisho ezincane okuthiwa quark. Gluon ensimini ebambe quark ndawonye, hhayi ubayekelela liphuke. Kukhona inkolelo yokuthi Quarks - akusiwona izinhlayiya aphansi kakhulu ezweni lethu. Kodwa inqobo nje uma abantu abanayo esanele lobuchwepheshe ukuze uqinisekise lesi.