Quantenmechanik

Cohen‐Tannoudji, Claude; Diu, Bernard; Laloë, Franck

doi:10.1515/9783110638738

Cited by 171 publications

(277 citation statements)

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“…This situation gets particularly simple if one considers the motion in a symmetric double well potential, as for example in the case of ammonia, where the three hydrogen atoms can be either at the left or the right side of the nitrogen atom. 21 [80] quantum mechanics, already developed by Hund [78], tells us that we can associate two different wavefunctions j1i and j2i with these two states. Both have the same energy E 0 .…”

Section: The Role Of Symmetry In Chemical Exchange Reactionsmentioning

confidence: 99%

“…In this situation the quantum mechanical density operatorr r has to be employed. For the coherent evolution of the density operator under the influence of a HamiltonianĤ H, the following differential equation is found [80] d dtr r ¼ ÀiĤ H;r r Â Ã (21.23) In this equation we have followed the NMR convention and set the constant " ¼ 1. This is equivalent to measuring energies in angular frequency units.…”

Section: The Density Matrixmentioning

confidence: 99%

“…The probability of penetrating the barrier depends on the energy of the incident particle and the width, shape and height of the potential barrier. For most potentials only approximate solutions, as for example the well-known Wenzel [91], Kramers [92], Brillouin [93] WKB approximation (see for example the textbook [80]), or numerical calculations of the transition probability are possible. Analytically solvable exceptions include rectangular potential steps and parabolic potentials.…”

Section: Incoherent Tunneling and The Bell Modelmentioning

confidence: 99%

“…80) which describes the exchange of the two nuclei in Liouville space. Its elements are the identity operatorÎ Î I I d and the permutation superoperatorP P P P 12 .…”

Section: Symmetry Effects On Nmr Lineshapes Of Intramolecular Dihydromentioning

confidence: 99%

“…[80,82]). As a result we find that in both the hydrogen and the deuterium case the ground state tunneling is describable by a pure spin tunnel Hamiltonian, which describes the tunnel splitting between the spatial pair of states of different symmetry.…”

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confidence: 99%

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Dihydrogen Transfer and Symmetry: The Role of Symmetry in the Chemistry of Dihydrogen Transfer in the Light of NMR Spectroscopy

Buntkowsky

Limbach

2006

Hydrogen‐Transfer Reactions

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Section: The Role Of Symmetry In Chemical Exchange Reactionsmentioning

confidence: 99%

Section: The Density Matrixmentioning

confidence: 99%

Section: Incoherent Tunneling and The Bell Modelmentioning

confidence: 99%

“…80) which describes the exchange of the two nuclei in Liouville space. Its elements are the identity operatorÎ Î I I d and the permutation superoperatorP P P P 12 .…”

Section: Symmetry Effects On Nmr Lineshapes Of Intramolecular Dihydromentioning

confidence: 99%

mentioning

confidence: 99%

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Dihydrogen Transfer and Symmetry: The Role of Symmetry in the Chemistry of Dihydrogen Transfer in the Light of NMR Spectroscopy

Buntkowsky

Limbach

2006

Hydrogen‐Transfer Reactions

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Applying Unconventional Spectroscopies to the Single‐Molecule Magnets, Co(PPh₃)₂X₂(X=Cl, Br, I): Unveiling Magnetic Transitions and Spin‐Phonon Coupling

Bone

Moseley

Liu

et al. 2021

Chemistry A European J

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Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single-molecule magnets (SMMs). Spin-phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin-phonon coupling in molecules is challenging. We have found that far-IR magnetic spectra (FIRMS) of Co(PPh 3 ) 2 X 2 (Co-X; X = Cl, Br, I) reveal rarely observed spin-phonon coupling as avoided crossings between magnetic and u-symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero-field split (ZFS) levels of the S = 3/2 electronic ground state were probed by INS, high-frequency and -field EPR (HFEPR), FIRMS, and frequency-domain FT terahertz EPR (FD-FT THz-EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) and g values. Ligand-field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities in Co-X, showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spinphonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.

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A Century Ago the Stern–Gerlach Experiment Ruled Unequivocally in Favor of Quantum Mechanics

Friedrich

2023

Israel Journal of Chemistry

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In 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a 2S state, with zero orbital and 12 ${{1 \over 2}}$ spin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.”

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Quantenmechanik

Cited by 171 publications

References 0 publications

Dihydrogen Transfer and Symmetry: The Role of Symmetry in the Chemistry of Dihydrogen Transfer in the Light of NMR Spectroscopy

Dihydrogen Transfer and Symmetry: The Role of Symmetry in the Chemistry of Dihydrogen Transfer in the Light of NMR Spectroscopy

Applying Unconventional Spectroscopies to the Single‐Molecule Magnets, Co(PPh₃)₂X₂(X=Cl, Br, I): Unveiling Magnetic Transitions and Spin‐Phonon Coupling

A Century Ago the Stern–Gerlach Experiment Ruled Unequivocally in Favor of Quantum Mechanics

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Quantenmechanik

Cited by 171 publications

References 0 publications

Dihydrogen Transfer and Symmetry: The Role of Symmetry in the Chemistry of Dihydrogen Transfer in the Light of NMR Spectroscopy

Dihydrogen Transfer and Symmetry: The Role of Symmetry in the Chemistry of Dihydrogen Transfer in the Light of NMR Spectroscopy

Applying Unconventional Spectroscopies to the Single‐Molecule Magnets, Co(PPh3)2X2(X=Cl, Br, I): Unveiling Magnetic Transitions and Spin‐Phonon Coupling

A Century Ago the Stern–Gerlach Experiment Ruled Unequivocally in Favor of Quantum Mechanics

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Applying Unconventional Spectroscopies to the Single‐Molecule Magnets, Co(PPh₃)₂X₂(X=Cl, Br, I): Unveiling Magnetic Transitions and Spin‐Phonon Coupling