The hydrogen atom in a uniform magnetic field — An example of chaos

Friedrich, Harald; Wintgen, Hieter

doi:10.1016/0370-1573(89)90121-x

Cited by 650 publications

(507 citation statements)

References 129 publications

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“…As mentioned above, this behaviour has been experimentally observed in the recurrence spectra of hydrogen and other Rydberg atoms in a magnetic field [9,10,11]. The dynamical interpretation of such experiments and of the results shown in Fig.…”

Section: Discussionsupporting

confidence: 75%

“…First, an initial wavefuntion localized in configuration space results from an expansion of several hundred energy eigenstates ψ E k (r). Second, each of these eigenstates contains several hundred thousand components on the numerical basis, obtained from the diagonalization of very large (but sparse) Hamiltonian matrices [9,11]. Third the integration of Eq.…”

Section: De Broglie-bohm Trajectoriesmentioning

confidence: 99%

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Can Bohmian trajectories account for quantum recurrences having classical periodicities?

Matzkin

2007

Physics Letters A

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Quantum systems in specific regimes display recurrences at the period of the periodic orbits of the corresponding classical system. We investigate the excited hydrogen atom in a magnetic field -a prototypical system of 'quantum chaos' -from the point of view of the de Broglie Bohm (BB) interpretation of quantum mechanics. The trajectories predicted by BB theory are computed and contrasted with the time evolution of the wavefunction, which shows pronounced features at times matching the period of closed orbits of the classical hydrogen in a magnetic field problem.Individual BB trajectories do not possess these periodicities and cannot account for the quantum recurrences. These recurrences can however be explained by BB theory by considering the ensemble of trajectories compatible with an initial statistical distribution, although none of the trajectories of the ensemble are periodic, rendering unclear the dynamical origin of the classical periodicities.

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Section: Discussionsupporting

confidence: 75%

Section: De Broglie-bohm Trajectoriesmentioning

confidence: 99%

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

Matzkin

2007

Physics Letters A

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“…While the problem of a Rydberg atom interacting with a strong magnetic field (the Diamagnetic Kepler Problem, DKP, also known as the Quadratic Zeeman Effect, QZE) has been fairly well understood as a result of sustained research in the past two decades [HRW89,FrWi89], the superficially similar scenario resulting from the addition of a perpendicular electric field -the so-called crossed field arrangement [S83,BS84,W&89,RFW91,vMDU94,vMU97a] -remains the least understood of all Rydberg problems. This is all the more remarkable in view of the prominence of the crossed fields in diverse areas of physics ranging from excitonic systems to plasmas and neutron stars.…”

Section: Introductionmentioning

confidence: 99%

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Berglund

Uzer²

2001

Foundations of Physics

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“…[8] or [9] for an overview). As a real physical system it was the topic of studies in experimental physics [10,11].…”

Section: The Hydrogen Atom In a Uniform Magnetic Fieldmentioning

confidence: 99%

ℏ expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

Cartarius

Main

2007

Annals of Physics

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We extend a theory of first order corrections to Gutzwiller's trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C 4v -symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the expansion method.

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The hydrogen atom in a uniform magnetic field — An example of chaos

Cited by 650 publications

References 129 publications

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

Can Bohmian trajectories account for quantum recurrences having classical periodicities?

Untitled

ℏ expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

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