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  • 1
    Electronic Resource
    Electronic Resource
    Molecular dipole moment charges from a new electronegativity scale (1985)
    s.l. : American Chemical Society
    Inorganic chemistry 24 (1985), S. 3631-3634 
    Details
    ISSN: 1520-510X
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/ic00216a031
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  • 2
    Electronic Resource
    Electronic Resource
    Construction of effective Hamiltonians for time-dependent phenomena from variational principles (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 3607-3613 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We develop a variational method for constructing the effective Hamiltonian that best propagates the state of a system, based on the minimization of a temporal error functional. As an illustrative example the procedure is used to derive the effective Hamiltonian in the time-dependent self-consistent-field method. The present variational approach is particularly useful to build the best effective Hamiltonian that is a linear combination of the generators of a Lie algebra. We explicitly consider systems having classical analogs with many degrees of freedom and calculate transition probabilities for a simple semiclassical model of the collinear collision between an atom and a diatomic molecule. We show that our variational approach is more general and accurate than the widely used local harmonic approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460811
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  • 3
    Electronic Resource
    Electronic Resource
    On the bilinear approximation for time-dependent Hamiltonians (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 1188-1193 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The transition probabilities for a one-dimensional harmonic oscillator with a time-dependent interaction potential are obtained. Two different bilinear approximations to the interaction potential are obtained by expanding it in Taylor series around two reference coordinate values, namely, the equilibrium position q0=0 and the expectation value of the coordinate q0=〈q〉, keeping only first- and second-order terms. The effect of the choice of q0 on the accuracy of the results is investigated for several values of the interaction potential parameters. The model posed by the semiclassical approach to the collision between a structureless particle and a harmonic oscillator via an exponential interaction potential is chosen as an illustrative example. The expansion around 〈q〉 is found to be related to an iterative procedure, based on Lie algebraic methods, recently proposed to treat time-dependent quantum-mechanical problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.458127
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Application of the Hill determinant method to the vibrational motion of diatomic molecules (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 7059-7061 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Hill determinant method is shown to be useful in obtaining the eigenvalues of central-field systems with potentials that can be expanded in the Taylor series. Some model potentials for diatomic molecules are considered as illustrative examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453351
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  • 5
    Electronic Resource
    Electronic Resource
    Transition probabilities for the driven harmonic oscillator (1987)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 87 (1987), S. 6206-6207 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A simple and straightforward method is presented for calculating transition probabilities for the driven harmonic oscillator. The procedure does not require the explicit calculation of neither the time-evolution operator nor the Green's function. As a result, a recurrence relation for the transition probabilities is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.453497
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  • 6
    Electronic Resource
    Electronic Resource
    Multidimensional harmonic oscillator matrix elements (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 5505-5508 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Multidimensional harmonic oscillator matrix elements of arbitrary products of exponentials for operators containing only linear and quadratic terms in the creation and annihilation operators are obtained. A simple and straightforward method is presented that leads to recurrence relations and generating functions for such matrix elements. Results are shown to be general enough to cover the cases of Franck–Condon overlaps, transition probabilities for time-dependent harmonic oscillators, and correlation functions for electronic spectra.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457553
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  • 7
    Electronic Resource
    Electronic Resource
    A generalized intermediate picture of quantal time evolution using operator algebraic methods. Application to translational–vibrational energy transfer in molecular collisions (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 3537-3541 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A method for solving the time-dependent Schrödinger equation in an intermediate picture defined by an effective time-dependent Hamiltonian is discussed. The state function in this intermediate picture is written as a linear combination of time-independent basis functions with time-dependent coefficients. It is shown how to use Lie algebraic methods to build the interaction potential in the intermediate picture and calculate physical observables. The construction of the interaction potential is explicitly discussed in the case of one degree of freedom with a classical coordinate analog. The effective Hamiltonian is obtained by expanding the potential energy function around a reference value of the coordinate. Effective Hamiltonians for He–H2 collisions obtained for equilibrium and average reference values of the vibrational coordinate of H2 are compared and the expansion convergence in the resulting intermediate pictures are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459775
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  • 8
    Electronic Resource
    Electronic Resource
    Calculation of vibrational transition probabilities in molecular collisions: A recursive algebraic procedure (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 924-928 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The vibrational energy transfer in collinear collisions between diatomic molecules is studied by means of a recursive algebraic approach applicable to several degrees of freedom. Introducing classical relative trajectories the problem is reduced to solving the Schrödinger equation with a time-dependent bilinear Hamiltonian. On using the equations of motion for the creation and annihilation operators, simple recurrence relations for the transition amplitudes are obtained. Transition probabilities between several vibrational states are calculated for N2+O2 to illustrate the advantages of the computational approach for high vibrational quantum numbers.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.457143
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  • 9
    Electronic Resource
    Electronic Resource
    Comment on: The Magnus expansion for the harmonically driven harmonic oscillator (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 88 (1988), S. 490-491 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The exponential time-evolution operator for the harmonically driven harmonic oscillator is exactly obtained from the equations of motion for the coordinate and momentum in the Heisenberg representation. The convergence of the Magnus expansion is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.454483
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  • 10
    Electronic Resource
    Electronic Resource
    Perturbation theory free from secular terms for the equations of motion of anharmonic oscillators (2001)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 4739-4748 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We develop a time–independent perturbation theory in operator form for the equations of motion of classical and quantum-mechanical anharmonic oscillators. The method focuses on the frequency of the motion in the former case and in a frequency operator in the latter, producing a power series in a small coupling constant. The resulting expressions are free from secular instabilities that commonly appear in perturbation treatments of nonlinear problems. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1402175
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