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  2. J-coupling - Wikipedia

    en.wikipedia.org/wiki/J-coupling

    where J jk is the J-coupling tensor, a real 3 × 3 matrix. It depends on molecular orientation, but in an isotropic liquid it reduces to a number, the so-called scalar coupling . In 1D NMR, the scalar coupling leads to oscillations in the free induction decay as well as splittings of lines in the spectrum.

  3. Karplus equation - Wikipedia

    en.wikipedia.org/wiki/Karplus_equation

    where J is the 3 J coupling constant, is the dihedral angle, and A, B, and C are empirically derived parameters whose values depend on the atoms and substituents involved. [3] The relationship may be expressed in a variety of equivalent ways e.g. involving cos 2φ rather than cos 2 φ —these lead to different numerical values of A , B , and C ...

  4. Angular momentum coupling - Wikipedia

    en.wikipedia.org/wiki/Angular_momentum_coupling

    In quantum mechanics, angular momentum coupling is the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta. For instance, the orbit and spin of a single particle can interact through spin–orbit interaction, in which case the complete physical picture must include spin–orbit coupling.

  5. Term symbol - Wikipedia

    en.wikipedia.org/wiki/Term_symbol

    Racah notation is basically a combination of LS or Russell–Saunders coupling and J 1 L 2 coupling. LS coupling is for a parent ion and J 1 L 2 coupling is for a coupling of the parent ion and the excited electron. The parent ion is an unexcited part of the atom.

  6. Magnetic inequivalence - Wikipedia

    en.wikipedia.org/wiki/Magnetic_inequivalence

    This kind of simplication is enhanced as the instrumental magnetic field is increased, since the field-independent differences between coupling constants or between a coupling constant and zero appear proportionately smaller on the δ (ppm) scale, and since the field-dependent quantity (ν A −ν X)/J AX is magnified.

  7. Coupling constant - Wikipedia

    en.wikipedia.org/wiki/Coupling_constant

    The dependence of a coupling g(μ) on the energy-scale is known as "running of the coupling". The theory of the running of couplings is given by the renormalization group , though it should be kept in mind that the renormalization group is a more general concept describing any sort of scale variation in a physical system (see the full article ...

  8. Total angular momentum quantum number - Wikipedia

    en.wikipedia.org/wiki/Total_angular_momentum...

    The relation between the total angular momentum vector j and the total angular momentum quantum number j is given by the usual relation (see angular momentum quantum number) ‖ ‖ = (+) The vector's z -projection is given by j z = m j ℏ {\displaystyle j_{z}=m_{j}\,\hbar } where m j is the secondary total angular momentum quantum number ...

  9. 3-j symbol - Wikipedia

    en.wikipedia.org/wiki/3-j_symbol

    A system of two angular momenta with magnitudes j 1 and j 2 can be described either in terms of the uncoupled basis states (labeled by the quantum numbers m 1 and m 2), or the coupled basis states (labeled by j 3 and m 3). The 3-j symbols constitute a unitary transformation between these two bases, and this unitarity implies the orthogonality ...