Effective disappearance of degenerating energy levels

Chabanov, V. M.; Zakhariev, B. N.; Brandt, Siegmund; Dahmen, Hans Dieter; Stroh, Tilo

doi:10.1103/physreva.52.r3389

Cited by 13 publications

(12 citation statements)

References 4 publications

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“…In the case of unequal thresholds, there occurs a spatial separation of some block of V αβ (x), see Fig.5. This block is transparent and goes to infinity in the limit of the level degeneracy resembling one-channel annihilation [27]. This separated block, in contrast with the annihilation case, does not carry away any part of the bound states.…”

Section: Degeneracy Of Energy Levelsmentioning

confidence: 92%

See 1 more Smart Citation

Toward the Quantum Design of Multichannel Systems The Inverse Problem Approach

Chabanov¹,

Zakhariev²,

Амирханов³

2000

Annals of Physics

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The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of interaction matrices leading to the concentration of waves in a chosen partial channel and spatial localization are shown. The limiting instructive cases illustrating different phenomena which ooccur with the combination of 'incompatible' properties are considered. For example, the scattering solutions with different resonance widths at the same energy for the same interaction are revealed. Analogously, a 'paradoxical' coexistence of both strong reflection and absolute transparency is explained. The case of the violation of 'natural' asymptotic behavior of partial wave function is demonstrated : it has a greater damping decrement for the channel with a lower threshold. Peculiarities of the multichannel periodic structures, bound states embedded into continuum, resonance tunneling and degeneracy of states are described.

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Section: Degeneracy Of Energy Levelsmentioning

confidence: 92%

“…We have discovered [27] the phenomenon of "effective annihilation" of degenerating states. These states must both be equal, as solutions of the same equation with the same boundary conditions, and simultaneously orthogonal as different states.…”

Section: Degeneracy Of Energy Levelsmentioning

confidence: 99%

Toward the Quantum Design of Multichannel Systems The Inverse Problem Approach

Chabanov¹,

Zakhariev²,

Амирханов³

2000

Annals of Physics

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“…We transform this potential according to the expressions given, e.g., in Refs. [3] and [5]. By deleting and restoring a bound state at energy E k , with the eigenfunction ψ k , via SUSYQM, we derive a singleparameter family of isospectral potentials U SS (λ k , z) [5]:…”

Section: Theoretical Considerationsmentioning

confidence: 99%

Multiparameter optimization of optical nonlinearities in semiconductor quantum wells by supersymmetric quantum mechanics

et al. 2001

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“…The exact formulae for symmetrical transformations of the initial potential well v(x) which shift only the nth level, and the corresponding wavefunctions were given in Pöschel and Trubovitz (1987). These formulae have been generalized (Chabanov et al 1995) to the case of the whole x line as well as to the case when there is a continuous spectrum as well as a discrete spectrum. These formulae are placed in section 2.3 for reference in order not to distract attention from the most important qualitative aspects of the theory.…”

Section: Shifts Of Energy Levelsmentioning

confidence: 99%

“…With decreasing ψ 1 at the centre there occurs also comparative sinking of the potential (see figure 1(d ) and one of potentials in figure 1(c) where a local minimum begins to appear in the middle of v). Gradually ψ 1 and ψ 2 are pressed into the infinite potential walls (effective 'disappearance' of states relative to the main middle well, see Chabanov et al (1995)). Meanwhile the first and last half-oscillations of all other states are separated by growing barriers inside the same special narrow wells at the vertical potential walls where they become shorter and shorter with vanishing amplitudes and gradually 'disappear' altogether with their two outermost knots under the barriers.…”

Section: Shifts Of Ground Statesmentioning

confidence: 99%

New situation in quantum mechanics (wonderful potentials from the inverse problem)

Zakhariev

Chabanov

1997

Inverse Problems

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Every physicist interested in nonrelativistic wave mechanics can now gain a deeper insight into quantum intuition. This is possible thanks to the advance in the theories of the inverse problem and supersymmetry which provides numerous new classes of exactly solvable models and instructive and clear illustrations revealing the fundamental elements of the coupling between potentials and observables; how to change the disposition of bound states on the energy scale (to shift, create or destroy the spectral levels) and in space by a special choice of potential perturbation. This theory explains the algorithms to control scattering features and wave motion over the lattices (e.g. crystal or discrete variable numbering channels). The best of thousands of corresponding 'quantum pictures' are selected here. The predictive power of the acquired intuition allows us to go beyond the scope of the exact models used for its elaboration.

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Effective disappearance of degenerating energy levels

Cited by 13 publications

References 4 publications

Toward the Quantum Design of Multichannel Systems The Inverse Problem Approach

Toward the Quantum Design of Multichannel Systems The Inverse Problem Approach

Multiparameter optimization of optical nonlinearities in semiconductor quantum wells by supersymmetric quantum mechanics

New situation in quantum mechanics (wonderful potentials from the inverse problem)

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