Zur Quantentheorie der Molekeln

Born, Max; Heisenberg, W.

doi:10.1002/andp.19273892002

Cited by 4,280 publications

(2,169 citation statements)

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“…One is connected with the Planck mass (Planck length, Planck time) and characterises gravitation, the other scale is connected with the non-gravitational matter fields. This fact can direct one's attention to a well-known method for the treatment of molecules such as the Born-Oppenheimer (BO) approach [12].…”

Section: Introductionmentioning

confidence: 99%

The Born–Oppenheimer method, quantum gravity and matter

Kamenshchik

Tronconi

Venturi

2017

Class. Quantum Grav.

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Abstract. We illustrate and examine diverse approaches to the quantum matter-gravity system which refer to the Born-Oppenheimer (BO) method. In particular we first examine a quantum geometrodynamical approach introduced by other authors in a manner analogous to that previously employed by us, so as to include back reaction and non-adiabatic contributions. On including such effects it is seen that the unitarity violating effects previously found disappear. A quantum loop space formulation (based on a hybrid quantisation, polymer for gravitation and canonical for matter) also refers to the BO method. It does not involve the classical limit for gravitation and has a highly peaked initial scalar field state. We point out that it does not resemble in any way to our traditional BO approach. Instead it does resemble an alternative, canonically quantised, non BO approach which we have also previously discussed.

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Section: Introductionmentioning

confidence: 99%

The Born–Oppenheimer method, quantum gravity and matter

Kamenshchik

Tronconi

Venturi

2017

Class. Quantum Grav.

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“…Combining the results of Subsections 3.1.1 and 3.1.2, the full Hamiltonian H JT SO for a single-mode 2 E × e JT system in complex representation reads as 65 52) where…”

Section: The E × E Vibronic Hamiltonian With So Couplingmentioning

confidence: 96%

“…3,52 The basic idea of this approximation is the separation of the electronic and the nuclear motions. Since the mass of an electron is small compared to that of the nuclei and the electrons therefore move quickly, the change in the nuclear positions can be considered to be negligible when calculating electronic wavefunctions.…”

Section: The Born-oppenheimer Approximationmentioning

confidence: 99%

Jahn–Teller and spin–orbit coupling effects in transition-metal trifluorides

et al. 2011

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“…The present communication is concerned with the problem of calculating the rotation-vibration energies and the absorption intensities of a triatomic molecule from the effective nuclear potential energy function and the dipole moment surfaces within the Born-Oppenheimer approximation (Born & Oppenheimer 1927). There are at least two astrophysical applications of such calculations:…”

Section: Introductionmentioning

confidence: 99%

The MORBID Method

Jensen¹

1994

International Astronomical Union Colloquium

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I n t r o d u c t i o nThe present communication is concerned with the problem of calculating the rotation-vibration energies and the absorption intensities of a triatomic molecule from the effective nuclear potential energy function and the dipole moment surfaces within the Born-Oppenheimer approximation (Born & Oppenheimer 1927). There are at least two astrophysical applications of such calculations: -Detailed spectra of triatomic molecules can be computed under the conditions prevailing in stellar atmospheres and compared with observed spectra. -Such spectra can also be used for constructing a wavenumber-dependent absorption coefficient which can be employed for opacity calculations as outlined, for example, by J0rgensen & Jensen (1993).In the Born-Oppenheimer approximation (Born k, Oppenheimer 1927), the rovibronic energies of a molecule are calculated in two steps: -In the first step, the nuclei are held fixed in space, and the Schrodinger problem for the electrons (which interact with the "clamped" nuclei and with each other through Coulomb forces) is solved for many different nuclear geometries. The energy eigenvalue obtained in this calculation, taken as a function of the nuclear coordinates (which we denote as R n here), is the Born-Oppenheimer potential energy function V(R"). -The second step is the solution of the Schrodinger equation for the nuclear motion,where T n is the operator representing the kinetic energy of the nuclei, ip n (R n ) is a nuclear wavefunction, and E ne is the corresponding energy eigenvalue.* Guest professor 1992-93. On leave from Physikalisch

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Zur Quantentheorie der Molekeln

Abstract: 1) Bei der Diskussion der Grundlagen dieser Arbeit hat uns Hr. Dr. P. Jordan durch wertvolle Bemerkungen unterstutzt, wofiir wir ihm unsern Dank eum Ausdruck bringen mochten.2) H.

Cited by 4,280 publications

References 8 publications

The Born–Oppenheimer method, quantum gravity and matter

The Born–Oppenheimer method, quantum gravity and matter

Jahn–Teller and spin–orbit coupling effects in transition-metal trifluorides

The MORBID Method

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