Video: Puas yog Hamiltonian commute nrog angular momentum?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Thaum ib tug particle nyob rau hauv tus ntawm lub hauv paus (symmetrical) muaj peev xwm, ces L kev mus los nrog lub zog muaj zog V(r). Yog L kev mus los nrog Hamiltonian tus neeg teb xov tooj (kinetic zog ntxiv rau lub zog muaj peev xwm) ces tus angularmomentum thiab lub zog tuaj yeem paub ib txhij.
Ua li no, puas angular momentum commute nrog momentum?
Cov angular zog cov neeg ua haujlwm ua tsis yog kev mus los , tab sis nws tseem ua tau rau cov angularmomentum kom zero nyob rau hauv tag nrho peb cov lus qhia. Tab sis sai li sai tau angular zog nyob rau hauv txhua qhov kev taw qhia yog nonzero, tsuas yog ib qho ntawm angular zog tuaj yeem muaj qhov tseeb.
Ib yam li ntawd, angular momentum nyob rau hauv quantum mechanics yog dab tsi? Cov angular zog tus neeg teb xov tooj ua lub luag haujlwm tseem ceeb hauv txoj kev xav ntawm atomic physics thiab lwm yam quantum teeb meem nrog kev hloov symmetry. Hauv ob qho tib si classicaland quantum mechanical systems, angular zog (ua ke nrog linear lub zog thiab lub zog) yog ib qho ntawm peb qhov tseem ceeb ntawm kev txav.
Yog li ntawd, puas spin thiab angular momentum commute?
jeblack3 hais tias: Kov tsis yog tus angularmomentum ntawm ib tug particle. Tag nrho angular zog ntawm aparticle yog kiv ntxiv rau orbital angular zog . Theorbital feem tsis yog kev mus los nrog lub zog , mas kiv tiv thaiv ua.
Puas yog angular momentum neeg teb xov tooj Hermitian?
Angular Momentum Operators . Ntxiv mus, muab qhov ntawd thiab cov yog Cov neeg ua haujlwm Hermitian , nws yog yooj yim pom tias cov kuj Hermitian . Qhov no yog qhov tseem ceeb, txij li tsuas yog Cov neeg ua haujlwm Hermitian tuaj yeem sawv cev rau lub cev hloov pauv inquantum mechanics (saib Sect. 4.6).
Pom zoo:
Dab tsi yog qhov muaj txiaj ntsig ntawm angular momentum quantum tooj L?
Lub Angular Momentum quantum tooj (l) piav qhia cov duab ntawm lub orbital. Qhov tso cai qhov tseem ceeb ntawml ntau ntawm 0 txog n - 1. Qhov sib nqus quantum tooj (ml) piav qhia txog kev taw qhia ntawm lub orbital inspace
Yuav ua li cas koj thiaj paub tias angular momentum yog kev txuag?
Ib yam li linear momentum tau txais kev cawmdim thaum tsis muaj lub zog sab nraud, lub zog angular yog qhov tsis tu ncua lossis khaws cia thaum lub net torque yog xoom. Yog tias qhov hloov pauv ntawm lub zog angular Δ L yog xoom, ces lub angular momentum yog tas li; so, → L = constant L → = constant (when net τ=0)
Puas yog angular momentum yog axial vector?
Axial vectors yog vector cross khoom ntawm qhov chaw vectors. Piv txwv li, angularmomentum L = r × v thiab torque T = r × F yog axialvectors
Qhov piv txwv ntawm angular momentum yog dab tsi?
Piv txwv ntawm kev txuag ntawm Angular Momentum Xav txog ib tug spinning skater. Lwm qhov piv txwv nrov ntawm kev txuag ntawm lub zog angular yog tus neeg tuav lub tsheb kauj vab tig ntawm lub rooj zaum tig. Tus neeg ntawd tig hla lub tsheb kauj vab, ua rau nws tig mus rau qhov sib txawv, raws li qhia hauv qab no
Dab tsi yog qhov derivative ntawm angular momentum?
Qhov tseem ceeb sib npaug Velocity ntawm qhov nruab nrab ntawm pawg ntawm dov khoom vCM=Rω Derivative of angular momentum equals torque d→ldt=∑→τ Angular momentum of a system of particles → L = → l1 + → l2 + ⋯ + → lN For a system of particles, derivative of angular momentum equals torque d → Ldt = ∑ → τ Angular momentum ntawm lub cev rotating nruj L = I ω