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  • 1
    Digitale Medien
    Digitale Medien
    Rotation operator approach to spin dynamics and the Euler geometric equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 6424-6429 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The rotation operator approach proposed previously is applied to spin dynamics in a time-varying magnetic field. The evolution of the wave function is described, and that of the density operator is also treated in terms of a spherical tensor operator base. It is shown that this formulation provides a straightforward calculation of accumulated phases and probabilities of spin transitions and coherence evolutions. The technique focuses, not on the rotation matrix, but on the three Euler angles and its characteristic equations are equivalent to the Euler geometric equations long known to describe the motion of a rigid body. The method usually depends on numerical calculations, but analytical solutions exist in some situations. In this paper, as examples, a hyperbolic secant pulse is solved analytically, and a Gaussian-shaped pulse is calculated numerically.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.468405
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  • 2
    Digitale Medien
    Digitale Medien
    Dynamics of single spin systems under arbitrary amplitude modulated fields (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 4673-4683 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: Using a spherical tensor operator basis a general method of solution to the time evolution of the spin density matrix for a spin of arbitrary magnitude I is given. Rather than using time ordering techniques, we present an integral equations approach for calculating the effects of arbitrary pulse shapes. The method is shown to provide a rapidly converging perturbation expansion which is useful in explaining many pulse shapes. In particular, a simple recipe for the calculation of the magnetization results from this technique. The successive terms in the perturbation expansion avoid multiple commutators such as are encountered in the Magnus expansion of the propagator. These terms are given simply as integrals of the pulse shape function. The examples of the Bloch–Siegert problem and the exact dynamics of a spin interacting with a rotating rf field combined with an isotropic relaxation and a regeneration mechanism are presented in the context of the method of transformations in Liouville space.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.452830
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  • 3
    Digitale Medien
    Digitale Medien
    The Wei–Norman Lie-algebraic technique applied to field modulation in nuclear magnetic resonance (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 2108-2123 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: By implementing the Wei–Norman Lie algebra approach, this paper focuses on the development of a new method of solution to the quantum Liouville equation for NMR field modulation. First, the general method is reviewed and discussed for systems of any finite dimensional Lie algebra. The theory is then applied to arbitrary time-dependent Zeeman interactions [or SU(2) Hamiltonians] in which the complete arbitrary spin I≥1/2 density operator problem reduces to a Riccati equation. Novel exact analytical solutions of the complete spin density operator for a class of temporal field modulations are obtained. In particular, a spherical tensor operator basis is used to expand the density operator, and the solutions retain the physically appealing form of Wigner rotations with time-modulated rotation angles which are special functions with well known analytical properties. The exact solutions include the frequency swept hyperbolic secant pulse shapes, as well as any exponentially modulated amplitude pulse. In contrast to all other existing formulations, the present treatment provides the first known examples of exactly soluble nonrectangular pulse shapes for all resonance off-set, all field amplitudes, all time and valid for all spin I≥1/2. In addition, from the underlying Riccati equation, a new series solution for the complete spin density matrix is given which is valid for any well-behaved field modulations. Spin inversion profiles are also calculated for exponentially decaying pulses. These show applications to selective excitation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.457071
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  • 4
    Digitale Medien
    Digitale Medien
    Relaxation of anisotropically oriented I=3/2 nuclei in the multipole basis: Evolution of the second rank tensor in the double quantum filtered nuclear magnetic resonance experiment (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 7372-7380 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The relaxation of an I=3/2 spin system in an anisotropic environment characterized by a finite residual quadrupolar splitting ωq is modeled by analytically solving for the density operator from Redfield's relaxation theory. The resulting equations are cast into the multipole basis in order to describe the tensorial components of the spin density matrix. Included in the relaxation matrix are off-diagonal elements J1 and J2, which account for anisotropic systems with ωq values less than the width of the resonant line. With the Wigner rotation matrices simulating hard pulses, the response to an arbitrary pulse sequence can be determined. An analytical expression for the response to the double quantum filtered (DQF) pulse sequence (π/2)−(τ/2)−π−(τ/2)−θ−δ−θ−AQ for θ=π/2 is presented, showing explicitly the formation of a second rank tensor owing only to the presence of a finite ωq. This second rank tensor displays asymptotic behavior when the (reduced) quadrupole splitting is equal to either of the off-diagonal spectral densities J2 and J1. Line shape simulations for ωq values of less than a linewidth reproduce the general features of some recently reported 23Na DQF line shapes from biological systems. Distinct relaxation dynamics govern each of the tensorial components of the resonant signal revealing the influence of the experimental variables on the line shape.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.468295
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  • 5
    Digitale Medien
    Digitale Medien
    Equilibrium theory of r-mer fluids (1981)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 85 (1981), S. 1264-1266 
    Details
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/j150609a035
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  • 6
    Digitale Medien
    Digitale Medien
    Theory of pure r-mers in the Guggenheim approximation (1981)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 85 (1981), S. 3153-3160 
    Details
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/j150621a031
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  • 7
    Digitale Medien
    Digitale Medien
    Automated extraction of spin coupling topologies from 2D NMR correlation spectra for protein proton resonance assignment (1993)
    s.l. : American Chemical Society
    Journal of chemical information and modeling 33 (1993), S. 475-489 
    Details
    ISSN: 1520-5142
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/ci00013a028
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  • 8
    Digitale Medien
    Digitale Medien
    CPA: Constrained partitioning algorithm for initial assignment of protein proton resonances from MQF-COSY (1993)
    s.l. : American Chemical Society
    Journal of chemical information and modeling 33 (1993), S. 490-500 
    Details
    ISSN: 1520-5142
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/ci00013a029
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  • 9
    Digitale Medien
    Digitale Medien
    Automation of protein 2D proton NMR assignment by means of fuzzy mathematics and graph theory (1993)
    s.l. : American Chemical Society
    Journal of chemical information and modeling 33 (1993), S. 668-682 
    Details
    ISSN: 1520-5142
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/ci00015a004
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  • 10
    Digitale Medien
    Digitale Medien
    Double Molecules in Gases (1965)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 69 (1965), S. 4422-4423 
    Details
    Quelle: ACS Legacy Archives
    Thema: Chemie und Pharmazie , Physik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1021/j100782a517
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