Related papers: Shape invariance in phase space
A second shape invariance property of the two-dimensional generalized Morse potential is discovered. Though the potential is not amenable to conventional separation of variables, the above property allows to build purely algebraically part…
We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler…
We consider two families of extensions of the oscillator in a $d$-dimensional constant-curvature space and analyze them in a deformed supersymmetric framework, wherein the starting oscillator is known to exhibit a deformed shape invariance…
Supersymmetry, shape invariance, exact solubility, and the factorization method are often studied together in the literature. At the dawn of these topics confusion was present in regards to their scope of applicability and the relation…
We examine shape invariant potentials (excluding those that are obtained by scaling) in supersymmetric quantum mechanics from the stand-point of periodic orbit theory. An exact trace formula for the quantum spectra of such potentials is…
Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations…
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable…
We extensively investigate two-step shape invariance in the framework of N-fold supersymmetry. We first show that any two-step shape-invariant system possesses type A 2-fold supersymmetry with an intermediate Hamiltonian and thus has…
According to the principle of relativity, the equations describing the laws of physics should have the same forms in all admissible frames of reference, i.e., form-invariance is an intrinsic property of correct wave equations. However, so…
Shape dynamics is a reframing of canonical general relativity in which time reparametrization invariance is "traded" for a local conformal invariance. We explore the emergence of Lorentz invariance in this model in three contexts: as a…
We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. {\bf 62}, 092101 (2021)] in the classical and quantum formalisms, by introducing the effect of the mass function in both kinetic…
The procedure proposed recently by J.Bougie, A.Gangopadhyaya and J.V.Mallow to study the general form of shape invariant potentials in one-dimensional Supersymmetric Quantum Mechanics (SUSY QM) is generalized to the case of Higher Order…
This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
The existence of a novel enlarged shape invariance property valid for some rational extensions of shape-invariant conventional potentials, first pointed out in the case of the Morse potential, is confirmed by deriving all rational…
We introduce a geometric formulation of quantum indeterminacy from which the standard uncertainty inequalities emerge as necessary consequences. Our approach is based on convex geometry in phase space and on methods from symplectic…
We present a conformally invariant generalized form of the free particle action by connecting the wave and particle aspects through gravity. Conformal invariance breaking is introduced by choosing a particular configurat$ of dynamical…
Size-invariant shape transformation is a technique of changing the shape of a domain while preserving its sizes under the Lebesgue measure. In quantum confined systems, this transformation leads to so-called quantum shape effects in the…
In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…