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Orthonormal polynomial projection quantization: an algebraic eigenenergy bounding method
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
The ability to generate tight eigenenergy bounds for low dimension bosonic or ferminonic, hermitian or non-hermitian, Schrödinger operator problems is an important objective in the computation of quantum systems. Very few ...
Linearised coherent states for non-rational SUSY extensions of the harmonic oscillator
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
In this work, we derive two equivalent non-rational extensions of the quantum harmonic oscillator using two different supersymmetric transformations. For these extensions, we built ladder operators as the product of the ...
Generalized three-body harmonic oscillator system: ground state
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
In this work we report on a 3-body system in a d−dimensional space ℝd with a quadratic harmonic potential in the relative distances rij = |ri −rj| between particles. Our study considers unequal masses, different spring ...
Time-dependent mass oscillators: constants of motion and semiclasical states
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
This work reports the construction of constants of motion for a family of time-dependent mass oscillators, achieved by implementing the formalism of form-preserving point transformations. The latter allows obtaining a ...
Photonic graphene under strain with position-dependent gain and loss
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
We work with photonic graphene lattices under strain with gain and loss, modeled by the Dirac equation with an imaginary mass term. To construct such Hamiltonians and their solutions, we use the free-particle Dirac equation ...
From quartic anharmonic oscillator to double well potential
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
Quantum quartic single-well anharmonic oscillator Vao(x) = x2 + g2x4 and double-well anharmonic oscillator Vdw(x) = x2(1−gx)2 are essentially one-parametric, they depend on a combination (g2ℏ). Hence, these problems are ...
Time-dependent step-like potential with a freezable bound state in the continuum
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
In this work, we construct a time-dependent step-like potential supporting a normalizable state with energy embedded in the continuum. The potential is allowed to evolve until a stopping time ti, where it becomes static. ...
About the time evolution of coherent electron states in monolayers of boron allotropes
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
In this paper, we theoretically analyze the massless Dirac fermion dynamics in twodimensional monolayers of boron allotropes, 8B and 2BH − pmmn borophene, interacting with external electric and magnetic fields. We study ...
Modified Korteweg-de Vries equation as a system with benign ghosts
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
We consider the modified Korteweg-de Vries equation, uxxx + 6u2ux + ut = 0, and explore its dynamics in spatial direction. Higher x derivatives bring about the ghosts. We argue that these ghosts are benign, i.e., the ...
Quantization of rationally deformed Morse potentials by Wronskian transforms of Romanovski-Bessel polynomials
(České vysoké učení technické v PrazeCzech Technical University in Prague, 2022)
The paper advances Odake and Sasaki’s idea to re-write eigenfunctions of rationally deformed Morse potentials in terms of Wronskians of Laguerre polynomials in the reciprocal argument. It is shown that the constructed ...