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  • 1
    Electronic Resource
    Electronic Resource
    Resonances in a box (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 103-117 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We investigate a numerical method for studying resonances in quantum mechanics. We prove rigorously that this method yields accurate approximations to resonance energies and widths for shape resonances in the semiclassical limit. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533124
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  • 2
    Electronic Resource
    Electronic Resource
    Semiclassical Dynamics¶with Exponentially Small Error Estimates (1999)
    Springer
    Communications in mathematical physics 207 (1999), S. 439-465 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract: We construct approximate solutions to the time–dependent Schrödinger¶equation for small values of ħ. If V satisfies appropriate analyticity and growth hypotheses and , these solutions agree with exact solutions up to errors whose norms are bounded by for some C and γ〉0. Under more restrictive hypotheses, we prove that for sufficiently small T ′, implies the norms of the errors are bounded by for some C ′, γ′〉0, and σ 〉 0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002200050732
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  • 3
    Electronic Resource
    Electronic Resource
    High order corrections to the time-dependent Born-Oppenheimer approximation. II: Coulomb systems (1988)
    Springer
    Communications in mathematical physics 117 (1988), S. 387-403 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the dynamics of molecular systems with Coulomb forces. We prove that if the nuclear masses are proportional to ε−4, then certain solutions to the time dependent Schrödinger equation have asymptotic expansions to arbitrarily high order in powers of ε, as ε ↘ 0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01223372
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  • 4
    Electronic Resource
    Electronic Resource
    A time dependent Born-Oppenheimer approximation (1980)
    Springer
    Communications in mathematical physics 77 (1980), S. 1-19 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider the dynamics of a quantum mechanical system which consists of some particles with large masses and some particles with small masses. As we increase the large masses to infinity we obtain the following results: The particles of smaller mass move adiabatically and determine an effective potential in which the heavier particles move semiclassically. Our methods can be applied to diatomic molecules with Coulomb forces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01205036
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  • 5
    Electronic Resource
    Electronic Resource
    Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps (1991)
    Springer
    Communications in mathematical physics 136 (1991), S. 433-449 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider a smooth operator-valued functionH(t,δ) that has two isolated non-degenerate eigenvaluesE A (t,δ) andE B (t,δ) for δ〉0. We assume these eigenvalues are bounded away from the rest of the spectrum ofH(t,δ), but have an avoided crossing with one another with a closest approach that isO(δ) as δ tends to zero. Under these circumstances, we study the small ε limit for the adiabatic Schrödinger equation $$i\varepsilon \frac{{\partial \psi }}{{\partial t}} = H(t,\varepsilon ^{1/2} )\psi .$$ We prove that the Landau-Zener formula correctly describes the coupling between the adiabatic states associated with the eigenvaluesE A (t,δ) andE B (t,δ) as the system propagates through the avoided crossing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099068
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  • 6
    Electronic Resource
    Electronic Resource
    High order corrections to the time-independent Born-Oppenheimer approximation II: Diatomic Coulomb systems (1988)
    Springer
    Communications in mathematical physics 116 (1988), S. 23-44 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the bound states of diatomic molecular systems. We prove that if the nuclear masses are proportional to ε−4 then certain eigenvalues and eigenvectors of the Hamiltonian have asymptotic expansions to arbitrarily high order in powers of ε, as ε→0. The zeroth through fourth order terms in the expansions for the eigenvalues are those of the well-known Born-Oppenheimer approximation. The fifth order term is zero.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01239023
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  • 7
    Electronic Resource
    Electronic Resource
    A link between scattering resonances and dilation analytic resonances in few body quantum mechanics (1979)
    Springer
    Communications in mathematical physics 65 (1979), S. 181-188 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the (2 cluster)→(2 cluster) scattering amplitudes for classes of two, three, and four particle dilation analytic Schrödinger operators whose two-body potentials fall off exponentially. As functions of the energy, these amplitudes are shown to have meromorphic continuations on certain Riemann surfaces. We prove that all poles of these continuations are necessarily bound states or dilation analytic resonances [i.e., eigenvalues ofH(θ) for some θ].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01225148
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  • 8
    Electronic Resource
    Electronic Resource
    Born series for (2 cluster) → (2 cluster) scattering of two, three, and four particle Schrödinger operators (1979)
    Springer
    Communications in mathematical physics 66 (1979), S. 77-94 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We investigate elastic and inelastic (2 cluster) → (2 cluster) scattering for classes of two, three, and four body Schrödinger operators $$H = H_0 + \sum\limits_{i〈 j} {V_{ij} .} $$ Formulas are derived for those generalized eigenfunctions ofH which correspond asymptotically in the past to two freely moving clusters. With these eigenfunctions, we establish a formula for the (2 cluster) → (2 cluster)T-matrix and prove the convergence of a Born series for theT-matrix at high energy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01197746
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  • 9
    Electronic Resource
    Electronic Resource
    Electron energy level crossings in the time-dependent Born-Oppenheimer approximation (1990)
    Springer
    Theoretical chemistry accounts 77 (1990), S. 163-190 
    Details
    ISSN: 1432-2234
    Keywords: Born-Oppenheimer approximation ; Level crossings ; Adiabatic approximation ; Semiclassical approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary We summarize the results of a mathematical study of the time-dependent Born-Oppenheimer approximation near crossings of two non-degenerate electron energy surfaces. We illustrate our techniques by relatively simple examples that contain the essential ingredients of the general cases. We discuss all generic types of crossings of two non-degenerate electron energy surfaces.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01114678
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  • 10
    Book
    Book
    Molecular propagation through electron energy level crossings; 536 (1994)
    Providence, RI :AMS,
    Details
    Title: Molecular propagation through electron energy level crossings; 536
    Author: Hagedorn, George A.
    Publisher: Providence, RI :AMS,
    Year of publication: 1994
    Pages: 130 S.
    Series Statement: Memoirs of the American Mathematical Society 536
    Type of Medium: Book
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    Zuse Institute Berlin get availability status
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