New PDF release: A semilinear Schrödinger equation in the presence of a

By Arioli G., Szulkin A.

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This brings us to the more general question of how reliable the simple constituent picture should be expected to be and what further tests might be envisaged. 3 When does the quark model work? There is general agreement that the NRQM is a good phenomenology for bb¯ and c¯c states below their respective flavour thresholds. Taking c¯c as an example we have S-states (ηc , ψ, ψ(2S)), P-states (χ0,1,2 ) and a D-state (ψ(3772)), the last just above ¯ threshold. Their masses and the strengths of the E1 radiative transitions the D D between ψ(2S) and χ J are in reasonable accord with their potential model status.

The sharpest discoveries have involved narrow resonances: c¯s states, probably ¯ , D ∗ K¯ thresholds; and c¯c degenerate with the D o D ¯ ∗o 0+ , 1+ , lying just below D K threshold. These are superficially heavy-flavour states, but their attraction to these thresholds involves light quarks and links to a more general theme. First note [5] that the c¯c potential picture gets significant distortions from the D D threshold region, such that even the c¯c χ states can have 10% or more admixtures of meson pairs, or four-quark states, in their wave functions.

States where all flavours are identical can only be written in a symmetric form. States where one or more is distinct can be written with antisymmetric parts. Only when all three are distinct can a totally antisymmetric combination be written. 1. These are respectively antisymmetric (ρ) and symmetric (λ) under the exchange 1 ↔ 2 while they go into linear combinations of one another under 1, 2 ↔ 3. Thus we say they transform with mixed symmetry M S (λ) and M A (ρ) respectively. There is no agreed convention and we will use M S,A or the λ and ρ notation throughout this book.

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A semilinear Schrödinger equation in the presence of a magnetic field by Arioli G., Szulkin A.

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