<i>Quantum</i> <i>Mechanics</i>

Cohen‐Tannoudji, Claude; Diu, Bernard; Lalö, Franck; Crasemann, Bernd

doi:10.1119/1.11749

Cited by 420 publications

(298 citation statements)

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“…The symmetry-adapted operators are â 4d † , â 4g † , â 4d , â 4g , and â 5d † , â 5g † , â 5d , â 5g , respectively 25 for i ) 4, 5.…”

Section: Spectroscopic Hamiltonian Of C 2 H 2 Bendsmentioning

confidence: 99%

“…The remainder of the critical points problem is to solve the last two equations of (25)(26)(27)(28) for the actions J a , J b as the polyad number N b is continuously varied, holding the angles at the above combinations. A simplification comes from the observation that with the discrete ψ a , ψ b values, (28) can be rewritten as For the entire accessible range of J a , J b , and when ψ a , ψ b are constrained to values in (33)(34)(35)(36), the factor between the curly brackets was numerically verified to be always nonzero.…”

Section: Implementation Of the Bifurcation Analysismentioning

confidence: 99%

“…In particular, when (40) holds, the denominators in (27 and 28) vanish, and ψ a , ψ b are either infinite (on the edges of Figure 3 except the vertexes, and also the boundaries of the pseudopotential plots in Figure 4) or indeterminate (at the four vertexes, where no unique limit exists). The general definition (25)(26)(27)(28) therefore cannot be used to determine whether a boundary point is a critical point or not. A related situation is encountered in ref 13 in the case of single resonance Hamiltonians.…”

Section: Implementation Of the Bifurcation Analysismentioning

confidence: 99%

See 2 more Smart Citations

Bending Dynamics of Acetylene: New Modes Born in Bifurcations of Normal Modes

Tyng

Kellman

2006

J. Phys. Chem. B

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W This paper contains enhanced objects available on the Internet at http://pubs.acs.org/jpcbfk.Semiclassical techniques are used to analyze highly excited pure bending vibrational dynamics from spectra of C 2 H 2 . An analytic bifurcation approach is developed, based on critical points of a classical version of the quantum fitting Hamiltonian. At high energy four new types of anharmonic modes are born in bifurcations of the normal modes: local, orthogonal, precessional, and counter-rotator. Visual insight into their nature is obtained with the help of computer-generated three-dimensional animations. The connection between the local mode and the acetylene-vinylidene isomerization "reaction mode" is considered.

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“…The symmetry-adapted operators are â 4d † , â 4g † , â 4d , â 4g , and â 5d † , â 5g † , â 5d , â 5g , respectively 25 for i ) 4, 5.…”

Section: Spectroscopic Hamiltonian Of C 2 H 2 Bendsmentioning

confidence: 99%

Section: Implementation Of the Bifurcation Analysismentioning

confidence: 99%

Section: Implementation Of the Bifurcation Analysismentioning

confidence: 99%

See 1 more Smart Citation

Bending Dynamics of Acetylene: New Modes Born in Bifurcations of Normal Modes

Tyng

Kellman

2006

J. Phys. Chem. B

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“…This leads to a dispersion of the particles. In order to estimate the dispersion in the length of time considered, we note that for a Gaussian packet, for a minimum dispersion packet one has that the dispersion is [18],…”

Section: B a Modified Zurek Model With A More Realistic Interactionmentioning

confidence: 99%

Undecidability and the Problem of Outcomes in Quantum Measurements

2009

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We argue that it is fundamentally impossible to recover information about quantum superpositions when a quantum system has interacted with a sufficiently large number of degrees of freedom of the environment. This is due to the fact that gravity imposes fundamental limitations on how accurate measurements can be. This leads to the notion of undecidability: there is no way to tell, due to fundamental limitations, if a quantum system evolved unitarily or suffered wavefunction collapse. This in turn provides a solution to the problem of outcomes in quantum measurement by providing a sharp criterion for defining when an event has taken place. We analyze in detail in examples two situations in which in principle one could recover information about quantum coherence: a) "revivals" of coherence in the interaction of a system with the measurement apparatus and the environment and b) the measurement of global observables of the system plus apparatus plus environment. We show in the examples that the fundamental limitations due to gravity and quantum mechanics in measurement prevent both revivals from occurring and the measurement of global observables. It can therefore be argued that the emerging picture provides a complete resolution to the measurement problem in quantum mechanics.

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“…In order to deal with the high degree of degeneracy of this potential, it is convenient to introduce the (integer) radial and angular quantum numbers n r and l, which are positive or zero, with [31] n = 2n r + l.…”

Section: Modelmentioning

confidence: 99%

Boson-fermion coherence in a spherically symmetric harmonic trap

Miyakawa

Meystre

2005

Phys. Rev. A

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We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small compared to the level separation of the trap, only those fermions in the single shell with Fermi energy are coupled to the bosonic molecular field. Introducing a collective pseudo-spin operator formalism we show that this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum optics, with an additional pairing interaction. By exact diagonalization of the Hamiltonian, we examine the ground state and low excitations of the BoseFermi system, and study the dynamics of the coherent coupling between atoms and molecules. In a semiclassical description of the system, the pairing interaction between fermions is shown to result in a self-trapping transition in the photoassociation, with a sudden suppression of the coherent oscillations between atoms and molecules. We also show that the full quantum dynamics of the system is dominated by quantum fluctuations in the vicinity of the self-trapping solution.

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Quantum Mechanics

Cited by 420 publications

References 0 publications

Bending Dynamics of Acetylene: New Modes Born in Bifurcations of Normal Modes

Bending Dynamics of Acetylene: New Modes Born in Bifurcations of Normal Modes

Undecidability and the Problem of Outcomes in Quantum Measurements

Boson-fermion coherence in a spherically symmetric harmonic trap

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