12.07.2015 Views

II parcijalni ispit iz predmeta Kvantna mehanika I ZADACI - PMF

II parcijalni ispit iz predmeta Kvantna mehanika I ZADACI - PMF

II parcijalni ispit iz predmeta Kvantna mehanika I ZADACI - PMF

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Univerzitet u SarajevuOdsjek za f<strong>iz</strong>iku, Prirodno-matematički fakultet(c) Vremenski zavisna funkcija je data <strong>iz</strong>razom(Ψ(⃗r, t) = a 1 ψ 300 exp − i )( E 3t + a 2 ψ 311 exp − i )( E 3t + a 2 ψ 322 exp − i ) E 3t,tako da je očekivana vrijednost 〈r〉:∫ ∞ ∫〈r〉 = |Ψ(⃗r, t)| 2 r 3 drdΩ = a 2 10Ω∫ ∞0R 2 30r 3 dr + a 2 2∫ ∞0R 2 31r 3 dr + a 2 3∫ ∞0R 2 32r 3 dr .5

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