Factorization method and new potentials from the inverted oscillator

Bermúdez, David; Fernández, J C David

doi:10.1016/j.aop.2013.02.015

Cited by 47 publications

(39 citation statements)

References 42 publications

(82 reference statements)

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“…If we neglect the hard-wall boundary condition, the Hamiltonian will be exactly solvable for the conduction band (18) which corresponds to the inverted harmonic oscillator equation [61,62]. By performing elementary quantum mechanical approaches, we find the following eigenvalue relation for the wave function and corresponding energy eigenvalues in the conduction band…”

Section: B Double Quantum Well Solution In the Conduction Bandmentioning

confidence: 99%

Theory of strain in single-layer transition metal dichalcogenides

et al. 2015

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Strain engineering has emerged as a powerful tool to modify the optical and electronic properties of two-dimensional crystals. Here we perform a systematic study of strained semiconducting transition metal dichalcogenides. The effect of strain is considered within a full Slater-Koster tight-binding model, which provides us with the band structure in the whole Brillouin zone. From this, we derive an effective low-energy model valid around the K point of the BZ, which includes terms up to second order in momentum and strain. For a generic profile of strain, we show that the solutions for this model can be expressed in terms of the harmonic oscillator and double quantum well models, for the valence and conduction bands respectively. We further study the shift of the position of the electron and hole band edges due to uniform strain. Finally, we discuss the importance of spin-strain coupling in these 2D semiconducting materials.

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Section: B Double Quantum Well Solution In the Conduction Bandmentioning

confidence: 99%

Theory of strain in single-layer transition metal dichalcogenides

et al. 2015

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“…where ∆ = E − V * and ξ = √ 2νx. A pair of solutions exists for each energy value ∆, which can be expressed in terms of hypergeometric functions, see [75]. With an appropriate normalization the two solutions represent waves incident from the left and from the right, as shown in Figure 10.…”

Section: Tunneling and Hawking Radiationmentioning

confidence: 99%

Interactions resolve state-dependence in a toy-model of AdS black holes

Bzowski

Gnecchi

Hertog

2018

J. High Energ. Phys.

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We show that the holographic description of a class of AdS black holes with scalar hair involves dual field theories with a double well effective potential. Black hole microstates have significant support around both vacua in the dual, which correspond to perturbative degrees of freedom on opposite sides of the horizon. A solvable toy-model version of this dual is given by a quantum mechanical particle in a double well potential. In this we show explicitly that the interactions replace the state-dependence that is needed to describe black hole microstates in a low energy effective model involving the tensor product of two decoupled harmonic oscillators. A naive number operator signals the presence of a firewall but a careful construction of perturbative states and operators extinguishes this.

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“…whereû stands for any solution of the first equation (8). An alternative representation for the transformation functions involves parametric derivatives with respect to E [7].…”

Section: The Confluent Susy Algorithmmentioning

confidence: 99%

Recursive representation of Wronskians in confluent supersymmetric quantum mechanics

Contreras-Astorga¹,

Schulze-Halberg²

2017

J. Phys. A: Math. Theor.

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A recursive form of arbitrary-order Wronskian associated with transformation functions in the confluent algorithm of supersymmetric quantum mechanics (SUSY) is constructed. With this recursive form regularity conditions for the generated potentials can be analyzed. Moreover, as byproducts we obtain new representations of solutions to Schrödinger equations that underwent a confluent SUSY-transformation.

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Factorization method and new potentials from the inverted oscillator

Cited by 47 publications

References 42 publications

Theory of strain in single-layer transition metal dichalcogenides

Theory of strain in single-layer transition metal dichalcogenides

Interactions resolve state-dependence in a toy-model of AdS black holes

Recursive representation of Wronskians in confluent supersymmetric quantum mechanics

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