Get Grundkurs Theoretische Physik 5/1. Quantenmechanik - PDF

By Wolfgang Nolting

ISBN-10: 3540421149

ISBN-13: 9783540421146

Der beliebte Grundkurs Theoretische Physik deckt in sieben Bänden alle für das Diplom maßgeblichen Gebiete ab. Jeder Band vermittelt intestine durchdacht das im jeweiligen Semester nötige theoretische-physikalische Rüstzeug. Zahlreiche Übungsaufgaben mit ausführlichen Lösungen dienen der Vertiefung des Stoffes.

Der erste Teil des fünften Bandes beginnt mit einer induktiven Begründung der Quantenmechanik, um dann, nach einer Untersuchung und Zusammenstellung der formalen Grundlagen der Quantenmechanik, an einfachen Modellsystemen die neuen Konzepte und Begriffsbildungen zu illustrieren.

Die vorliegende neue Auflage wurde grundlegend überarbeitet und ergänzt. Sie ermöglicht durch die neue zweifarbige Darstellung einen sehr übersichtlichen und schnellen Zugriff auf den Lehrstoff.

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Phys. Rev. A, 80, 045802 (2009). 1 Preliminaries: Schr¨ odinger evolution operator, Heisenberg picture, SDEs The Schr¨odinger evolution operator U (tf , ti ) is defined by | ψ (tf ) = U (tf , ti ) | ψ (ti ) , where the state must satisfy the Schr¨ odinger equation d | ψ (t) = H | ψ (t) . dt Hence, we find the evolution equation i d (U (t, ti ) | ψ (ti ) ) = HU (t, ti ) | ψ (ti ) , dt d i U (t, ti ) | ψ (ti ) = HU(t, ti ) | ψ (ti ) , dt d 1 U (t, ti ) = HU (t, ti ) , U (ti , ti ) = 1. dt i If the Hamiltonian is constant, this can be solved straightforwardly via the operator exponential, i U (t, ti ) = exp [−iH (t − ti ) / ] .

2 2 Hence, in these simple cases, we have either a pure increase or a pure decrease in the cavity decay rate as the only net effect of the feedback. These can be understood as interferometric constructive/destructive interference of the output fields from the κb1 and κb2 cavity mirrors. We infer that since the external driving term (through mirror κb3 ) is unaffected, it should be possible to use ϕ to tune the average intracavity photon number. In particular, if we have a detuned driving field, we should be able to decrease the effective driving strength by decreasing the effective κb , and vice versa.

1). The (S, L, H) triple is thus simply r11 t21 (S, L, H) = t12 r22 0 0 , ,0 , where since the scattering matrix must be unitary, r11 t21 ∗ r11 t∗12 t12 r22 t∗21 ∗ r22 1 0 = 0 1 . A common example is the 50/50 beamsplitter: r11 t21 t12 r22 = √1 2 √1 2 − √12 √1 2 . Note that from a theoretical standpoint the phase convention we have chosen is arbitrary (for example, the transpose of this matrix could equally well represent a 50/50 beamsplitter), but in modeling an actual experimental setup the phases of the matrix elements will be determined by physical properties of the actual beamsplitting device.

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Grundkurs Theoretische Physik 5/1. Quantenmechanik - Grundlagen by Wolfgang Nolting


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