Dirac ta karshe. Dirac lissafi. Jimla filin ka'idar

Wannan labarin ya mayar da hankali a kan aikin na Paul Dirac lissafi wanda ƙwarai wadãtar da jimla makanikai. Yana bayyana ainihin Concepts zama dole mu fahimci jiki ma'anar lissafi, kazalika da hanyoyin da ta aikace-aikace.

Kimiyya da masana kimiyya

The mutum ba a hade tare da kimiyya, shi ne sanin samar da tsari a wasu sihiri da sakamako. The masana kimiyya, a cikin ra'ayi na mutane - shi cranks wanda magana da wani bakon harshe da kuma dan kadan m. Farawa matsahi na saba da bincike, da nisa daga kimiyya mutumin da zarar ya ce ya bai fahimci kimiyyar lissafi a makaranta. Kamar wancan mutumin a cikin titi ne masu garu kashe daga ilimin kimiyya, da kuma buƙatun mafi ilimi interlocutor yi magana sauki kuma mafi ilhama. Lalle ne, Paul Dirac lissafi muna tunani, maraba da.

na farko barbashi

A tsarin da al'amari ne ko da yaushe m m hankulansu. A zamanin d Girka, mutane sun lura da cewa marmara matakai, wanda ya dauki mai yawa kafa, canji siffar a kan lokaci, da kuma shawara da cewa: kowace ƙafarsa, ko sandal daukawa da shi wani kankanin bit na al'amarin. Wadannan abubuwa sun yanke shawarar kira "kwayoyin halitta", da cewa shi ne "basa". Sunan da ya rage, amma ya juya daga cewa kwayoyin zarra da barbashi cewa yin up atoms - wannan fili, hadaddun. Wadannan barbashi an kira na farko. An sadaukar da aikin da suka Dirac lissafi wanda a yarda ba kawai don bayyana juya daga wani electron, amma kuma bayar da shawarar gaban antielectron.

Kalaman-barbashi biyuntakar

A ci gaba da fasahar hotuna a makara karni na sha tara, entailed ba kawai fashion na imprinting kansa, abinci da kuma Cats, amma kuma ciyar da yiwuwa na kimiyya. Bayan samu irin wannan m kayan aiki a matsayin mai sauri hoto (yi tunani a baya daukan hotuna kai game 30-40 minti), masana kimiyya ya fara en sun mayar gyara da dama a jere.

Data kasance a lokacin ka'idar tsarin abubuwa iya ba a fili bayyana ko hasashen da a jere hadaddun kwayoyi. Da farko, sanannen gwaji na Rutherford ya nuna cewa zarra ba haka basa: zuciyarsa ya yi nauyi m tsakiya kusa wanda yayi sauki korau electrons. Sa'an nan aka gano radioactivity ya tabbatar da cewa da kwaya ba monolith, kuma aka yi sama da protons da neutrons. Kuma a sa'an nan da kusan lokaci daya samu na jimla da makamashi, da Heisenberg rashin tabbas manufa da kuma probabilistic yanayin na farko barbashi wuri ba impetus zuwa cin gaban wani tushen sabon kimiyya tsarin kula da nazari da suke kewaye da duniya. Wani sabon sashe - da kimiyyar lissafi na firamare barbashi.

Babban batun a alfijir na shekaru daga cikin manyan binciken a matsananci-kananan sikelin ya bayyana gaban na farko barbashi talakawa da kuma kalaman Properties.

Einstein ya tabbatar da cewa ko da imperceptible photon yana da wani taro, a matsayin m watsa wani bugun jini, wanda da dama a kan (haske matsa lamba sabon abu). A wannan yanayin, da yawa gwaje-gwajen a kan watsi da electrons a cikin crevices na ce a kalla suna da diffraction da tsangwama, shi ne peculiar kawai don kaɗa hadayar. A sakamakon haka, na yi shigar: da na farko barbashi a lokaci guda wani abu da wani taro da wani kalaman. Wannan ne, da taro na, sai ka ce, wani electron kamar yadda aka "smeared" a cikin makamashi kunshin ga kalaman Properties. Wannan manufa na kalaman-barbashi biyuntakar ya yarda ya bayyana da farko na duk dalilin da ya sa electron ba ya fada a cikin tsakiya, da kuma abin da dalilai wanzu a zarra ta kewayewa, da kuma mi} a tsakanin su ne ba zato. Wadannan mi da kuma samar da wani bakan musamman ga kowane abu. Next, na farko barbashi kimiyyar lissafi dole ne bayyana ya Properties na barbashi kansu, kazalika da interactions.

A kalaman aiki na da jimla lambobin

Erwin Schrödinger sanya wani abin mamaki da yau, iyalinsu m bude (a kan tushen da ya daga baya Pol Dirak gina ka'idarsa). Ya tabbatar da cewa, jihar na da wani na farko barbashi, misali, ya bayyana wani electron kalaman aiki ψ. By kanta, shi ba ya nufin wani abu, amma shi zai Square yiwuwar gano da electron a iyakancen batu na sarari. A wannan jiha na firamare barbashi a zarra (ko wani tsarin), an bayyana ta hudu jimla lambobi. Wannan babban (n), orbital (l), Magnetic (m) da kuma juya (m _s) lambobi. Sun nuna da kaddarorin na farko barbashi. Kamar yadda wani misalin, za ka iya kawo man block. Its halaye - nauyi, size, launi da kuma mai abun ciki. Duk da haka, da kaddarorin cewa bayyana na farko barbashi, ba za a iya gane lamirinsu, ya kamata su zama sane da ta cikin ilmin lissafi bayanin. Aiki Dirac lissafi ne - da mayar da hankali na wannan labarin ne kishin karshen, da yawan juya.

juya

Kafin a ci gaba kai tsaye zuwa lissafi, shi wajibi ne don bayyana abin da zai suturta da juya yawan m _s. Yana nuna nasu kusurwa lokacinta na electron, da sauran na farko barbashi. Wannan lambar ne ko da yaushe tabbatacce kuma iya daukar wani lamba darajar, sifili ko rabin darajar (ga m _s = 1/2 electron). Juya - size vector da daya kadai da ya bayyana da fuskantarwa da electron. Jimla filin ka'idar yana sanya juya tushen da musayar hulda, abin da ba ya da takwaransa a kullum ilhama makanikai. Juya yawan nuna yadda vector dole ne ya tũba zuwa zo ta asali jihar. An misali zai zama talakawa ball-aya alkalami (rubutun bangare zai bari tabbatacce shugabanci na vector). Wannan ta zo don ta asalin jiha, shi wajibi ne dõmin ka jũyar da 360 digiri. Wannan halin da ake ciki ya dace da baya daga 1. Lokacin da baya rabin, a matsayin electron juyawa dole ne 720 digiri. Saboda haka, ban da ilmin lissafi diraya, dole ne sun ɓullo da na sarari tunani su fahimci wannan dukiya. Just sama aikata da kalaman aiki. Shi ne babban "actor" Schrodinger lissafi da abin da ya bayyana jihar da kuma matsayi na na farko barbashi. Amma wannan dangantaka a asalin siffan ne aka yi nufi ga spinless barbashi. Bayyana jihar na electron iya kawai rike idan hakan na Schrödinger lissafi, wanda aka yi a cikin aikin na Dirac.

Bosons da fermions

Fermion - barbashi da rabin lamba juya darajar. Fermions ana shirya a tsarin (msl kwayoyin halitta) bisa ga Pauli wariya manufa: in kowace jiha ya kamata ba fiye da daya barbashi. Saboda haka, duk electron a zarra ne ɗan daban-daban daga duk wasu (wasu jimla yawan yana da ma'anoni daban-daban). Jimla filin ka'idar bayyana wani hali - bosons. Bã su da wani juya, da kuma duk iya lokaci guda a cikin wannan jiha. Aiwatar da wannan yanayin kira Bose-Einstein sandaro. Duk da fairly da kyau ya tabbatar da ka'idojin yiwuwar samun da shi, shi ne da gaske za'ayi a 1995 kadai.

Dirac lissafi

Kamar yadda muka ce a sama, Pol Dirak samu wani lissafi na gargajiya filin electron. Yana kuma bayyana matsayi da sauran fermions. A zahirin ma'ana da dangantaka ne hadaddun da multifaceted, kuma saboda da siffar ya zama mai yawa da muhimman hakkokin karshe. Form na lissafi ne kamar haka:

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

inda m - taro na fermions (musamman electrons), c - gudu daga haske, p _k - uku aiki lokacinta bangaren (da gatura x, y, z), H - trimmed Planck ta m, x da kuma t - uku na sarari tsarawa (ya yi daidai da gatura X , Y, Z) da kuma lokaci, bi da bi, da kuma ψ (x, t) - chetyrohkomponentnaya hadaddun kalaman aiki, α _{k (k} = 0, 1, 2, 3) - Pauli matrix. A karshen ne mikakke aiki da cewa aiki a kan kalaman aiki da sarari. Wannan dabara ne quite rikitarwa. Don fahimta akalla da aka gyara, wajibi ne a fahimci ainihin ma'anar jimla makanikai. Ya kamata ka ma su mallaki wata gagarumar ilmin lissafi ilmi to akalla san abin da a vector, matrix, da kuma sadarwa. Specialist nau'i na lissafi a ce ko da fiye da aka gyara. Wani mutum masani a nukiliya kimiyyar lissafi da kuma jimla makanikai saba da, gane muhimmancin wannan dangantaka. Duk da haka, dole ne mu yarda cewa Dirac lissafi da kuma Schrödinger - kawai na farko ka'idodinta ilmin lissafi bayanin irin matakai da faruwa a duniyar jimla yawa. Irfanin lissafin kimiyya, suka yanke shawarar su bada kansa ga na farko barbashi kuma su interactions, dole fahimci ainihin wadannan dangantakar a kan na farko da na biyu digiri. Amma wannan kimiyya ne m, kuma shi ne a cikin wannan yanki zai iya yin nasara ko da dorewar sunansa, assigning shi zuwa lissafi, hira ko dukiya.

A zahirin ma'anar lissafi

Kamar yadda muka alkawarta, mun gaya abin karshe ya ɓõye da Dirac lissafi ga electron. Da fari dai, wannan aboki ya bayyana cewa electron juya shi ne ½. Abu na biyu, bisa ga lissafi, da electron yana da wani muhimmi Magnetic lokacin. Daidai ne a cikin Bohr magneton (daya na farko Magnetic lokacin). Amma, mafi muhimmanci sakamakon samun wannan rabo da yake a cikin inconspicuous sadarwarka α _k. Kammalawa na Dirac lissafi daga Schrödinger lissafi dauki lokaci mai tsawo. Dirac farko zaton cewa wadannan aiki hana dangantaka. Tare da taimakon daban-daban ilmin lissafi dabaru ya yi kokarin ware su daga lissafi, amma bai yi nasara ba. A sakamakon haka, da Dirac lissafi ga free barbashi hada da hudu sadarwarka α. Kowace daga cikinsu wakiltar wani matrix [4x4]. Biyu dace da m taro na electron, wanda ya tabbatar da cewa akwai biyu arziki na ta juya. Wasu biyu ba wani bayani ga mummunan taro barbashi. A mafi asali sanin kimiyyar lissafi samar da wani mutum zuwa ga kammala da cewa ba shi yiwuwa a gaskiya. Amma a sakamakon gwajin da aka gano cewa na karshe biyu matrices ne mafita ga data kasance gaɓũɓuwa, electron m - anti-electron. Kamar yadda electron, positron (don haka ya kira wannan barbashi) yana da wani taro, amma cajin ne tabbatacce.

positron

Kamar yadda sau da yawa ya faru a zamanin binciken jimla Dirac a farko ba su yi imani nasu karshe. Ya bai yi kuskure ya fito fili ya buga Hasashen na wani sabon barbashi. Duk da haka, a cikin wani yawan takardun da symposia a kan daban-daban malamai sun jaddada yiwuwar ta zama, ko da yake ba a tsara. Amma nan da nan bayan janyewar wannan sanannen rabo positron aka gano a cosmic radiation. Saboda haka, ta zama an tabbatar empirically. Positron - na farko samu mutane antimatter kashi. Positron haife matsayin daya twin biyu (da wasu tagwaye - shi ne wani electron) a cikin hulda da photons da sosai high makamashi abu tsakiya a wani karfi lantarki filin. Ba Figures muke so ba (da kuma sha'awar karatu zai sami kansa dukan zama dole bayani). Duk da haka, yana da daraja jaddada cewa wannan shi ne wani cosmic sikelin. Don samar da ake bukata makamashi photons iya kawai supernova fashe da galactic collisions. su ne ma a cikin da dama dauke a cikin nuclei na zafi taurari, ciki har da rana. Amma wani mutum ko da yaushe o ƙarin wa amfani. A rushewa daga al'amarin, kuma antimatter ba mai yawa makamashi. Don shawo wannan tsari da kuma a saka shi ga amfãnin mutãne (misali, zai zama tasiri injuna na interstellar jiragen ruwa don warwarewa), mutane sun koyi su yi da protons a cikin dakin gwaje-gwaje.

A musamman, manyan accelerators (kamar LHC) iya ƙirƙirar electron-positron biyu. A baya can ma an ba da shawara cewa akwai ba kawai na farko antiparticles (a Bugu da kari ga electron su 'yan mafi), amma dukan antimatter. Ma wani karamin yanki na wani crystal na antimatter zai samar da makamashi duniya (watakila Kryptonite magabacin mutumi ya antimatter?).

Amma alas, halittar antimatter nuclei mutum fiye da hydrogen ba a rubuce a cikin san talikai. Duk da haka, idan mai karatu yana zaton cewa hulda da al'amarin (lura, shi ne abu, ba na wani guda electron) tare da positron warwarewa nan da nan ƙare, shi ne kuskure. Lokacin da positron deceleration a high gudun a wasu taya da wadanda ba sifili yiwuwa taso related electron-positron biyu, da ake kira positronium. Wannan samuwar yana da wasu kadarori na zarra har ma da ikon shiga cikin sinadaran halayen. Amma akwai wannan m jummai gajeren lokaci, sa'an nan kuma har yanzu shafe tare da watsi da biyu, da kuma a wasu lokuta, da kuma uku gamma haskoki.

disadvantages na lissafi

Duk da cewa ta hanyar wannan dangantaka aka gano da anti-electron da antimatter, shi yana da wani gagarumin drawback. Rubuta lissafai da kuma model gina bisa shi, ba su iya hango ko hasashen yadda barbashi an haife kuma hallaka. Wannan shi ne wani peculiar irony na jimla duniya: ka'idar, annabta haihuwar al'amari-antimatter nau'i-nau'i, ba zai iya mayalwaci bayyana wannan tsari. Wannan hasara da aka shafe ta a jimla filin ka'idar. By gabatar da quantization na filayen, wannan model bayyana su hulda, ciki har da halittar kuma da warwarewa daga na farko barbashi. By "jimla filin ka'idar" a wannan yanayin yana nufin wani sosai musamman ambatacce. Wannan shi ne wani yanki na kimiyyar lissafi da cewa karatu da hali na jimla filayen.

Dirac ta lissafi a cylindrical tsarawa

Don fara, bari ka san abin da a cylindrical tsara tsarin. Maimakon saba uku yardatayya perpendicular gatura domin sanin ainihin wurin da wani batu a sarari ta amfani da kwana, da radius da kuma tsawo. Wannan shi ne guda a matsayin iyakacin duniya daidaita tsarin a kan jirgin, amma kara na uku girma - tsawo. Wannan tsarin shi ne amfani a lokacin da ka na so ka bayyana ko su gudanar da bincike a surface tsakaitã game da daya axis. Jimla makanikai ne mai matukar amfani da m kayan aiki da za a iya rage girman da yawan dabarbari da lissafin. Wannan shi ne sakamako na axial fasali na electron girgije a zarra. A Dirac lissafi an warware a cylindrical tsarawa dan kadan daban fiye da saba a cikin tsarin, da kuma wani lokacin samar da m sakamakon. Alal misali, wasu aikace-aikace da matsalar kayyade hali na firamare barbashi (yawanci electrons) a cikin quantized fasalin irin filin warware lissafai zuwa cylindrical tsarawa.

Amfani da lissafai domin sanin tsarin da particulate

Wannan lissafi ya bayyana na farko barbashi: waɗannan da ba su kunshi ko karami abubuwa. Kimiyyar zamani ne iya auna Magnetic lokacin da high daidaituwa. Saboda haka, a mismatch lissafa ta amfani da Dirac lissafi dabi'u gwaje auna Magnetic lokacin za a kaikaice nuna hadaddun tsarin da barbashi. Ka tuna, wannan lissafi ya shafi fermions, su rabin lamba juya. rikitarwa tsarin protons da neutrons aka tabbatar da yin amfani da wannan lissafi. Kowace daga cikinsu ta ƙunshi ko da karami da aka gyara kira quarks. Gluon filin rike da quarks tare, ba ka sake su fada baya. Akwai ka'idar cewa quarks - wannan ba shi ne mafi firamare barbashi mu duniya. Amma idan dai mutane ba su da isasshen fasaha damar don tabbatar da wannan.