Kab lus no piav qhia txog kev ua haujlwm nthwv dej thiab nws lub ntsiab lus ntawm lub cev. Daim ntawv thov ntawm lub tswv yim no nyob rau hauv lub moj khaum ntawm Schrödinger kab zauv kuj raug txiav txim.
Kev tshawb fawb yog nyob rau ntawm qhov kev tshawb pom quantum physics
Thaum kawg ntawm lub xyoo pua puas xyoo, cov tub ntxhais hluas uas xav txuas lawv lub neej nrog kev tshawb fawb tau poob siab los ntawm kev ua physicists. Muaj kev xav tias txhua qhov tshwm sim twb tau pom thiab tsis tuaj yeem muaj kev cuam tshuam loj hauv cheeb tsam no. Tam sim no, txawm hais tias zoo li tag nrho ntawm tib neeg kev paub, tsis muaj leej twg yuav twv yuav raug hais li no. Vim tias qhov no tshwm sim ntau zaus: qhov tshwm sim lossis qhov tshwm sim tau kwv yees theoretically, tab sis tib neeg tsis muaj peev xwm thiab thev naus laus zis txaus los ua pov thawj lossis tsis lees paub lawv. Piv txwv li, Einstein tau kwv yees qhov kev tsis sib haum xeeb ntau dua li ib puas xyoo dhau los, tab sis nws tau los ua pov thawj lawv lub neej tsuas yog ib xyoos dhau los. Qhov no kuj siv tau rau lub ntiaj teb ntawm subatomic hais (xws li, xws li lub tswv yim xws li kev ua haujlwm nthwv dej siv rau lawv): kom txog thaum cov kws tshawb fawb pom tau tias cov qauv ntawm lub atom yog complex, lawv tsis tas yuav kawm txog tus cwj pwm ntawm cov khoom me me.
Spectra thiab photography
Push totxoj kev loj hlob ntawm quantum physics yog kev txhim kho cov tswv yim yees duab. Txog thaum pib ntawm lub xyoo pua nees nkaum, kev ntes cov duab yog cumbersome, siv sij hawm thiab kim: lub koob yees duab hnyav kaum kilograms, thiab cov qauv yuav tsum tau sawv ntsug rau ib nrab ib teev nyob rau hauv ib txoj hauj lwm. Tsis tas li ntawd, qhov yuam kev me me hauv kev tuav cov iav tsis yooj yim coated nrog cov duab emulsion ua rau cov ntaub ntawv poob tsis tau. Tab sis maj mam cov khoom siv tau sib dua, qhov nrawm nrawm - tsawg dua thiab tsawg dua, thiab tau txais cov ntawv luam tawm - ntau thiab zoo meej. Thiab thaum kawg, nws tau los ua kom tau txais ib qho spectrum ntawm cov khoom sib txawv. Cov lus nug thiab kev tsis sib haum xeeb uas tau tshwm sim hauv thawj qhov kev xav txog qhov xwm txheej ntawm spectra tau ua rau muaj kev tshawb fawb tshiab. Kev ua haujlwm nthwv dej ntawm ib qho particle thiab nws qhov sib npaug Schrödinger tau los ua lub hauv paus rau kev piav qhia lej ntawm tus cwj pwm ntawm microworld.
particle-yoj dual
Tom qab txiav txim siab tus qauv ntawm lub atom, cov lus nug tshwm sim: yog vim li cas cov hluav taws xob tsis poob ntawm lub nucleus? Tom qab tag nrho, raws li Maxwell qhov sib npaug, txhua qhov kev txav mus los ntawm cov khoom tawg, yog li, poob lub zog. Yog hais tias qhov no yog cov ntaub ntawv rau cov electrons nyob rau hauv lub nucleus, lub ntug raws li peb paub nws yuav tsis kav ntev. Nco qab tias peb lub hom phiaj yog yoj ua haujlwm thiab nws cov ntsiab lus txheeb cais.
Ib qho kev xav tsis zoo ntawm cov kws tshawb fawb tau los cawm: cov ntsiab lus tseem ceeb yog cov nthwv dej thiab cov khoom (corpuscles). Lawv cov khoom yog ob qho tib si huab hwm coj nrog lub zog thiab wavelength nrog zaus. Tsis tas li ntawd, vim muaj ob qho khoom tsis sib xws yav dhau los, cov khoom me me tau txais cov yam ntxwv tshiab.
Ib leeg yog ib qho nyuaj rau xav txog tig. Hauv ntiaj teb nome me, quarks, muaj ntau yam ntawm cov khoom uas lawv tau muab lub npe zoo kawg nkaus: tsw, xim. Yog tias tus nyeem ntawv ntsib lawv hauv phau ntawv ntawm quantum mechanics, cia nws nco ntsoov: lawv tsis yog txhua yam lawv zoo li thaum xub thawj siab ib muag. Txawm li cas los xij, yuav ua li cas piav qhia txog tus cwj pwm zoo li no, qhov twg txhua lub ntsiab lus muaj cov khoom txawv txawv? Cov lus teb yog nyob rau ntu tom ntej.
Schrödinger equation
Nrhiav lub xeev uas ib qho tseem ceeb (thiab, nyob rau hauv ib tug generalized daim ntawv, ib tug quantum system) nyob, tso cai rau Erwin Schrödinger qhov sib npaug:
i ħ[(d/dt) Ψ]=Ĥ ψ.
Cov npe hauv qhov piv no yog raws li hauv qab no:
- ħ=h/2 π, qhov twg h yog Planck qhov tas mus li.
- Ĥ - Hamiltonian, tag nrho lub zog tus neeg teb xov tooj ntawm qhov system.
- Ψ yog lub luag haujlwm nthwv dej.
Hloov cov kev tswj hwm uas qhov kev ua haujlwm no tau daws thiab cov xwm txheej raws li hom particle thiab thaj chaw uas nws nyob, ib tus tuaj yeem tau txais txoj cai ntawm kev coj tus cwj pwm hauv kev txiav txim siab.
Lub ntsiab lus ntawm quantum physics
Cia tus nyeem tsis txhob dag los ntawm qhov yooj yim ntawm cov lus siv. Cov lus thiab kab lus xws li "tus neeg ua haujlwm", "tag nrho lub zog", "unit cell" yog cov ntsiab lus ntawm lub cev. Lawv cov txiaj ntsig yuav tsum tau qhia meej cais, thiab nws yog qhov zoo dua los siv phau ntawv. Tom ntej no, peb yuav muab cov lus piav qhia thiab daim ntawv ntawm kev ua haujlwm nthwv dej, tab sis tsab xov xwm no yog kev tshuaj xyuas qhov xwm txheej. Yuav kom nkag siab tob txog lub tswv yim no, nws yog ib qho tsim nyog yuav tsum kawm cov cuab yeej ua lej ntawm ib qib.
Wave function
Nws qhia lejmuaj daim ntawv
|ψ(t)>=ʃ Ψ(x, t)|x> dx.
Kev ua haujlwm nthwv dej ntawm ib qho hluav taws xob lossis lwm yam khoom nruab nrab yog ib txwm piav qhia los ntawm Greek tsab ntawv Ψ, yog li qee zaum nws tseem hu ua psi-function.
Ua ntej koj yuav tsum nkag siab tias txoj haujlwm nyob ntawm txhua qhov haujlwm thiab sijhawm. Yog li Ψ(x, t) yog tiag Ψ(x1, x2… x , t). Ib qho tseem ceeb, txij li qhov kev daws teeb meem ntawm Schrödinger kab zauv nyob ntawm qhov kev sib koom ua ke.
Tom ntej no, nws yog qhov yuav tsum tau qhia meej tias |x> txhais tau tias lub hauv paus vector ntawm qhov kev sib koom ua ke xaiv. Ntawd yog, nyob ntawm seb qhov yuav tsum tau ua tiag tiag, lub zog lossis qhov tshwm sim |x> yuav zoo li | x1, x2, …, x >. Obviously, n kuj tseem nyob ntawm qhov tsawg kawg nkaus vector hauv paus ntawm qhov kev xaiv. Ntawd yog, hauv qhov chaw peb-dimensional ib txwm n=3. Rau cov neeg nyeem tsis paub, cia peb piav qhia tias tag nrho cov cim nyob ze ntawm qhov ntsuas x tsis yog ib qho kev xav xwb, tab sis kev ua lej tshwj xeeb. Nws yuav tsis tuaj yeem nkag siab nws yam tsis muaj kev suav lej nyuaj tshaj plaws, yog li peb cia siab tias cov neeg txaus siab yuav pom nws lub ntsiab lus rau lawv tus kheej.
Thaum kawg, yuav tsum piav qhia tias Ψ(x, t)=.
Lub cev qhov tseem ceeb ntawm nthwv dej ua haujlwm
Txawm hais tias tus nqi tseem ceeb ntawm qhov ntau, nws tus kheej tsis muaj qhov tshwm sim lossis lub tswv yim raws li nws lub hauv paus. Lub ntsiab lus ntawm lub cev ntawm yoj ua haujlwm yog qhov square ntawm nws tag nrho cov qauv. Cov mis zoo li no:
|Ψ (x1, x2, …, x , t)| 2=ω, qhov twg ω yog tus nqi ntawm qhov tshwm sim qhov ceev. Nyob rau hauv cov ntaub ntawv ntawm discrete spectra (es tsis yog tas mus li), tus nqi no tsuas yog ib tug tshwm sim.
Qhov tshwm sim ntawm lub cev lub ntsiab lus ntawm kev ua haujlwm nthwv dej
Lub ntsiab lus ntawm lub cev muaj qhov cuam tshuam loj heev rau tag nrho lub ntiaj teb quantum. Raws li nws tau pom tseeb los ntawm tus nqi ntawm ω, txhua lub xeev ntawm cov ntsiab lus tseem ceeb tau txais cov xim zoo nkauj. Qhov piv txwv pom tseeb tshaj plaws yog qhov kev faib tawm ntawm cov huab cua hluav taws xob hauv lub orbits ncig lub atomic nucleus.
Cia peb coj ob hom kev sib xyaw ntawm cov hluav taws xob hauv cov atoms nrog cov ntaub ntawv yooj yim tshaj plaws ntawm huab: s thiab p. Huab ntawm thawj hom yog spherical nyob rau hauv cov duab. Tab sis yog tias tus nyeem ntawv nco qab los ntawm cov phau ntawv qhia txog physics, cov huab cua hluav taws xob no yeej ib txwm piav qhia raws li qee yam ntawm qhov tsis pom tseeb ntawm cov ntsiab lus, thiab tsis yog qhov sib luag. Qhov no txhais tau hais tias ntawm ib qho kev ncua deb ntawm lub nucleus muaj ib cheeb tsam nrog lub siab tshaj plaws tshwm sim ntawm ntsib ib tug s-electron. Txawm li cas los xij, me ntsis ze dua thiab me ntsis ntxiv qhov tshwm sim no tsis yog xoom, nws tsuas yog tsawg dua. Nyob rau hauv cov ntaub ntawv no, rau p-electrons, cov duab ntawm lub electron huab yog depicted raws li ib tug me ntsis qhov muag plooj dumbbell. Ntawd yog, muaj qhov nyuaj ntawm qhov chaw uas qhov tshwm sim ntawm kev nrhiav ib qho hluav taws xob yog qhov siab tshaj. Tab sis txawm nyob ze rau qhov "dumbbell", ob qho tib si ntxiv thiab ze rau lub hauv paus, xws li qhov tshwm sim tsis sib npaug rau xoom.
Normalization ntawm nthwv dej ua haujlwm
Qhov kawg txhais tau hais tias yuav tsum ua kom lub zog ua haujlwm tsis zoo. Los ntawm normalization yog txhais tau tias xws li "tsim" ntawm qee qhov tsis muaj, uas nws muaj tseebib co ratio. Yog hais tias peb xav txog spatial coordinates, ces qhov tshwm sim ntawm kev nrhiav ib tug muab particle (ib tug electron, piv txwv li) nyob rau hauv lub ntiaj teb no uas twb muaj lawm yuav tsum sib npaug zos rau 1. Cov mis zoo li no:
ʃV Ψ Ψ dV=1.
Yog li, txoj cai ntawm kev txuag hluav taws xob tau ua tiav: yog tias peb tab tom nrhiav ib qho hluav taws xob tshwj xeeb, nws yuav tsum nyob hauv ib qho chaw. Txwv tsis pub, kev daws qhov sib npaug Schrödinger tsuas yog tsis muaj txiaj ntsig. Thiab nws tsis muaj teeb meem yog tias cov khoom no nyob hauv lub hnub qub lossis hauv qhov khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob khoob
Ib me ntsis siab dua peb tau hais tias qhov sib txawv ntawm qhov kev ua haujlwm nyob ntawm kuj tseem tuaj yeem ua haujlwm tsis yog qhov chaw. Nyob rau hauv cov ntaub ntawv no, normalization yog nqa tawm nyob rau hauv tag nrho cov tsis nyob rau hauv lub functionality.
Instant travel: dag lossis kev muaj tiag?
Hauv quantum mechanics, cais lej los ntawm lub ntsiab lus ntawm lub cev yog qhov nyuaj heev. Piv txwv li, lub quantum tau qhia los ntawm Planck rau qhov yooj yim ntawm kev qhia lej ntawm ib qho kev sib npaug. Tam sim no lub hauv paus ntsiab lus ntawm kev tsis sib haum xeeb ntawm ntau qhov ntau thiab cov ntsiab lus (lub zog, lub zog ntawm lub zog, daim teb) qhia txog txoj hauv kev niaj hnub rau kev kawm ntawm microworld. Ψ kuj muaj qhov paradox no. Raws li ib qho ntawm cov kev daws teeb meem ntawm Schrödinger kab zauv, nws muaj peev xwm hais tias quantum lub xeev ntawm lub system hloov tam sim ntawd thaum lub sij hawm ntsuas. Qhov tshwm sim no feem ntau yog hu ua kev txo qis lossis kev sib tsoo ntawm yoj ua haujlwm. Yog tias qhov no ua tau hauv qhov tseeb, quantum systems muaj peev xwm txav ntawm qhov nrawm tsis kawg. Tab sis qhov txwv ceev rau cov khoom tiag tiag ntawm peb lub Ntiaj Tebimmutable: tsis muaj dab tsi tuaj yeem taug kev nrawm dua li lub teeb. Qhov tshwm sim no yeej tsis tau sau tseg, tab sis tseem tsis tau muaj peev xwm rov hais dua nws theoretical. Nyob rau tib lub sijhawm, tej zaum, qhov kev tsis sib haum xeeb no yuav raug daws: tib neeg yuav muaj qhov ntsuas uas yuav kho qhov tshwm sim, lossis yuav muaj kev ua lej uas yuav ua pov thawj qhov tsis sib xws ntawm qhov kev xav no. Muaj ib qho kev xaiv thib peb: tib neeg yuav tsim qhov tshwm sim, tab sis tib lub sijhawm lub hnub ci yuav poob rau hauv lub qhov dub dub.
Wave muaj nuj nqi ntawm ntau qhov system (hydrogen atom)
Raws li peb tau hais thoob plaws hauv tsab xov xwm, psi-function piav qhia txog ib qho piv txwv. Tab sis ntawm kev soj ntsuam ze dua, hydrogen atom zoo li lub kaw lus tsuas yog ob qhov (ib qho tsis zoo electron thiab ib qho zoo proton). Lub zog nthwv dej ntawm hydrogen atom tuaj yeem piav qhia ua ob-particle lossis los ntawm tus neeg teb xov tooj ceev matrix. Cov matrices no tsis yog qhov txuas ntxiv ntawm psi muaj nuj nqi. Hloov chaw, lawv qhia cov ntawv xov xwm ntawm qhov tshwm sim ntawm kev nrhiav ib qho hauv ib thiab lwm lub xeev. Nws yog ib qho tseem ceeb kom nco ntsoov tias qhov teeb meem tsuas yog daws tau rau ob lub cev tib lub sijhawm. Qhov ntom ntom matrices muaj feem xyuam rau cov khub ntawm cov khoom, tab sis tsis tuaj yeem ua rau ntau lub tshuab, piv txwv li, thaum peb lossis ntau lub cev sib cuam tshuam. Nyob rau hauv qhov tseeb no, ib qho zoo kawg li zoo sib xws tuaj yeem taug qab ntawm feem ntau " ntxhib" mechanics thiab "zoo" quantum physics. Yog li ntawd, ib tug yuav tsum tsis txhob xav tias txij li thaum quantum mechanics tshwm sim, cov tswv yim tshiab tsis tuaj yeem tshwm sim hauv cov physics zoo tib yam. Qhov nthuav yog zais qab ib qholos ntawm kev ua lej manipulations.
