Energy spectrum of a confined two-dimensional particle in an external magnetic field

Rosas, R.; Riera, R.; Marı́n, J. L.; León, H.

doi:10.1119/1.1302718

Cited by 10 publications

(15 citation statements)

References 4 publications

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“…We note in passing that these eigenvalues have originally been gained for a single electron in a magnetic field and an additional harmonic confinement. In the case ω 0 = 0, i. e. without the external confinement, for m positive or zero, the spectrum reduces to the so-called Landau levels E rel = (2n r + 1)hω L , which are infinitely degenerate with respect to the angular momentum quantum number, see also [12]. Separability is still given, also with the Coulomb term.…”

Section: Wkb Spectramentioning

confidence: 99%

“…Due to the fact that exact analytic solutions of the Schödinger equation are limited to an infinite set of discrete oscillator frequencies [3,5], also approximate analytic solutions have been sought for. Apart from the perturbation theoretic ones in 2d, mentioned above, also semiclassical approaches have been taken which rely on the Wentzel-Kramers-Brillouin (WKB) [12], respectively the Einstein-Brillouin-Keller (EBK) quantization rules [13]. Most notably, in 2d and with an additional magnetic field this has been done analytically by Klama and Mishchenko [14].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Großmann¹,

Kramer²

2011

J. Phys. A: Math. Theor.

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For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the propagator lead to eigenvalues of the same accuracy as WKB calculations with Langer correction. The latter are restricted to integrable systems, however, whereas the timedependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and is extendable to arbitrary shapes of the potential.

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Section: Wkb Spectramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Großmann¹,

Kramer²

2011

J. Phys. A: Math. Theor.

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“…1 Another example that occurs in a variety of condensed matter problems is a particle confined to two dimensions in an external magnetic field. 2 In nuclear physics, the Interacting Boson Model classifies many nuclei according to one of three dynamical symmetries. 3 But, what should be done if the system is nowhere near any of the exact limits?…”

Section: Introductionmentioning

confidence: 99%

Confined one-dimensional harmonic oscillator as a two-mode system

Gueorguiev

Rau

Draayer

2006

American Journal of Physics

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Spontaneous symmetry breakdown in non-relativistic quantum mechanics Am. J. Phys. 80, 891 (2012) Understanding the damping of a quantum harmonic oscillator coupled to a two-level system using analogies to classical friction Am. J. Phys. 80, 810 (2012) Relation between Poisson and Schrödinger equations Am. J. Phys. 80, 715 (2012) Comment on "Exactly solvable models to illustrate supersymmetry and test approximation methods in quantum mechanics," Am. J. Phys. 79, 755-761 (2011) Am. J. Phys. 80, 734 (2012) The uncertainty product of position and momentum in classical dynamics Am.The one-dimensional harmonic oscillator in a box is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a ͑one-dimensional͒ box. Each of the limits has a characteristic spectral structure describing the two different excitation modes of the system. Near these limits perturbation theory can be used to find an accurate description of the eigenstates. Away from the limits it is necessary to do a matrix diagonalization because the basis-state mixing that occurs is typically large. An alternative to formulating the problem in terms of one or the other basis set is to use an "oblique" basis that uses both sets. We study this alternative for the example system and then discuss the applicability of this approach for more complex systems, such as the study of complex nuclei where oblique-basis calculations have been successful.

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“…Another two-mode system of interest is a particle confined in two dimensions by an external magnetic field. This system is interesting because there is a lifting of the infinite degeneracy of Landau like states due to the confinement [40]. 10 A simple explanation of this effect is that the unperturbed energies E 0 n are such that E 0 n > δE 1 n .…”

Section: Discussion Of the Toy Model Resultsmentioning

confidence: 99%

“…In the forthcoming chapters, we consider |0 to represent closed-shell nuclei. For example, 16 O is the closed-shell nucleus when we study nuclei in the valence sd-shell; 40 Ca is the closed-shell nucleus when we study nuclei in the valence pf -shell.…”

Section: Hamiltonian In Second Quantized Formmentioning

confidence: 99%

Mixed-Mode Shell-Model Calculations

Gueorguiev¹,

Draayer²

2002

AIP Conference Proceedings

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A one-dimensional harmonic oscillator in a box is used to introduce the oblique-basis concept. The method is extended to the nuclear shell model by combining traditional spherical states, which yield a diagonal representation of the usual single-particle interaction, with collective configurations that track deformation. An application to 24Mg, using the realistic two-body interaction of Wildenthal, is used to explore the validity of this mixed-mode shell-model scheme. Specifically, the correct binding energy (within 2% of the full-space result) as well as low-energy configurations that have greater than 90% overlap with full-space results are obtained in a space that spans less than 10% of the full-space. The theory is also applied to lower pf-shell nuclei, 44Ti-48Ti and 48Cr, using the Kuo-Brown-3 interaction. These nuclei show strong SU(3) symmetry breaking due mainly to the single-particle spin-orbit splitting. Nevertheless, the results also show that yrast band B(E2) values are insensitive to fragmentation of the SU(3) symmetry. Specifically, the quadrupole collectivity as measured by B(E2) strengths remains high even though the SU(3) symmetry is rather badly broken. The IBM and broken-pair models are considered as alternative basis sets for future oblique-basis shell-model calculations.Comment: 3 pages, no figures, summary of a poster present at the Nuclear Structure Conference: Mapping the Triangle. Grand Teton National Park, Wyoming USA, May 22-25, 200

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Energy spectrum of a confined two-dimensional particle in an external magnetic field

Cited by 10 publications

References 4 publications

Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Spectra of harmonium in a magnetic field using an initial value representation of the semiclassical propagator

Confined one-dimensional harmonic oscillator as a two-mode system

Mixed-Mode Shell-Model Calculations

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