Higher order supersymmetric truncated oscillators

We construct ladder operators,C andC † , for a multi-step rational extension of the harmonic oscillator on the half plane, x ≥ 0. These ladder operators connect all states of the spectrum in only infinite-dimensional representations of their polynomial Heisenberg algebra. For comparison, we also construct two different classes of ladder operator acting on this system that form finitedimensional as well as infinite-dimensional representations of their respective polynomial Heisenberg algebras. For the rational extension, we construct the position wavefunctions in terms of exceptional orthogonal polynomials. For a particular choice of parameters, we construct the coherent states, eigenvectors ofC with generally complex eigenvalues, z, as superpositions of a subset of the energy eigenvectors. Then we calculate the properties of these coherent states, looking for classical or non-classical behaviour. We calculate the energy expectation as a function of |z|. We plot position probability densities for the coherent states and for the even and odd cat states formed from these coherent states. We plot the Wigner function for a particular choice of z. For these coherent states on one arm of a beamsplitter, we calculate the two excitation number distribution and the linear entropy of the output state. We plot the standard deviations in x and p and find no squeezing in the regime considered. By plotting the Mandel Q parameter for the coherent states as a function of |z|, we find that the number statistics is sub-Poissonian. * scott.hoffmann@uqconnect.edu.au 2

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“…This is in full agreement with [36], after noting that their Hamiltonians are one half of ours. The first (state adding) path uses…”

Section: A the Untruncated Oscillatorsupporting

confidence: 91%

Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator

Hoffmann

Hussin

Marquette

et al. 2019

Journal of Mathematical Physics

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“…For NGC 2287 we have used the UBV photometry of Ianna et al (1987) and fit a E B V ( ) -of 0.035±0.025 with an assumed solar metallicity. For NGC 3532 we have used the UBV photometry of Fernandez & Salgado (1980) and fit a E B V ( ) -of 0.04±0.025 with an assumed solar metallicity. Lastly, for NGC 2168 we have used the UBV photometry of Sung & Bessell (1999).…”

Section: Color-color Analysismentioning

confidence: 99%

TWO MASSIVE WHITE DWARFS FROM NGC 2323 AND THE INITIAL–FINAL MASS RELATION FOR PROGENITORS OF 4–6.5 M_⊙*

Cummings¹,

Kalirai²,

Tremblay³

et al. 2016

ApJ

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We observed a sample of 10 white dwarf candidates in the rich open cluster NGC 2323 (M50) with the Keck LowResolution Imaging Spectrometer. The spectroscopy shows eight to be DA white dwarfs, with six of these having high signal-to-noise ratio appropriate for our analysis. Two of these white dwarfs are consistent with singly evolved cluster membership, and both are high mass ∼1.07 M e , and give equivalent progenitor masses of 4.69 M e . To supplement these new high-mass white dwarfs and analyze the initial-final mass relation (IFMR), we also looked at 30 white dwarfs from publicly available data that are mostly all high-mass ( 0.9 M e ). These original published data exhibited significant scatter, and to test if this scatter is true or simply the result of systematics, we have uniformly analyzed the white dwarf spectra and have adopted thorough photometric techniques to derive uniform cluster parameters for their parent clusters. The resulting IFMR scatter is significantly reduced, arguing that mass-loss rates are not stochastic in nature and that within the ranges of metallicity and mass analyzed in this work mass loss is not highly sensitive to variations in metallicity. Lastly, when adopting cluster ages based on Y 2 isochrones, the slope of the high-mass IFMR remains steep and consistent with that found from intermediate-mass white dwarfs, giving a linear IFMR from progenitor masses between 3 and 6.5 M e . In contrast, when adopting the slightly younger cluster ages based on PARSEC isochrones, the high-mass IFMR has a moderate turnover near an initial mass of 4 M e .

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“…When two systems are related through supersymmetry, they share nearly identical spectra and states from one system may be transformed into states of the other system by the action of differential operators known as supercharges. In one-dimensional quantum mechanics, supersymmetry has been used to study a plethora of new potentials including partners of: the Rosen-Morse potentials [3,4], the truncated oscillator [5][6][7], and the singular oscillator [8]. In higherdimensional quantum systems, supersymmetry is less explored, though coherent states for the two-dimensional infinite well and its coordinate separable supersymmetric partners have been discussed [9].…”

Section: Introductionmentioning

confidence: 99%

Coherent states of the two-dimensional non-separable supersymmetric Morse potential

Moran

Hussin

2021

Eur. Phys. J. Plus

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Supersymmetry is a fundamental feature of a quantum theory described by a supersymmetric Hamiltonian comprised of several quantum mechanical Hamiltonians with different potentials that allows us to relate information about the states and spectra of the constituent Hamiltonians. In this paper we reconstruct Ioffe's set of states for the singular non-separable two-dimensional Morse potential using supersymmetry from a non-degenerate set of states constructed for the initial separable Morse Hamiltonian. We define generalised coherent states, compute their uncertainty relations, and we find that the singularity in the partner Hamiltonian significantly affects the localisation of the coherent state wavefunction.

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Higher order supersymmetric truncated oscillators

Cited by 10 publications

References 36 publications

Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator

Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator

TWO MASSIVE WHITE DWARFS FROM NGC 2323 AND THE INITIAL–FINAL MASS RELATION FOR PROGENITORS OF 4–6.5 M_⊙*

Coherent states of the two-dimensional non-separable supersymmetric Morse potential

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Higher order supersymmetric truncated oscillators

Cited by 10 publications

References 36 publications

Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator

Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator

TWO MASSIVE WHITE DWARFS FROM NGC 2323 AND THE INITIAL–FINAL MASS RELATION FOR PROGENITORS OF 4–6.5 M⊙*

Coherent states of the two-dimensional non-separable supersymmetric Morse potential

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TWO MASSIVE WHITE DWARFS FROM NGC 2323 AND THE INITIAL–FINAL MASS RELATION FOR PROGENITORS OF 4–6.5 M_⊙*