Related papers: Shape invariance in phase space
Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution.…
A phase field model for dealing with shape instabilities in fluid membrane vesicles is presented. This model takes into account the Canham-Helfrich bending energy with spontaneous curvature. A dynamic equation for the phase-field is also…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
The self-similar potentials are formulated in terms of the shape-invariance. Based on it, a coherent state associated with the shape-invariant potentials is calculated in case of the self-similar potentials. It is shown that it reduces to…
Can we change the shape of a domain without altering its sizes? By introducing a size-invariant shape transformation, we propose the existence and explore the consequences of a new type of physical effect appearing at the quantum scales,…
The association of the variational method with supersymmetric quantum mechanics through an ansatz for the superpotential is reviewed and the approximate energy spectra of non-exactly solvable potentials, such like the Hulthen, the Morse and…
Since the particles such as molecules, atoms and nuclei are composite particles, it is important to recognize that physics must be invariant for the composite particles and their constituent particles, this requirement is called particle…
An algebro-operator approach, called shape invariant potential method, of constructing generalized coherent states for photon-added particle system is presented. Illustration is given on Poschl-Teller potential.
We formulate the structure of spectral invariance in shape invariance single and double well potentials using derivative invariance.
Using the Wigner distribution function, we analyze the behavior on phase space of generalized coherent states associated with the Morse potential (Morse-like coherent states). Within the f-deformed oscillator formalism, such states are…
Deformations of quantum field theories which preserve Poincar\'e covariance and localization in wedges are a novel tool in the analysis and construction of model theories. Here a general scenario for such deformations is discussed, and an…
We present a novel extension of the concept of scars for the wave functions of classically chaotic few-body systems of identical particles with rotation and permutation symmetry. Generically there exist manifolds in classical phase space…
The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study whether the spheroidal equations have the shape-invariance property. Expanding the super-potential term by term in the parameter alpha and solving it, we…
We formulate and study the set of coupled nonlinear differential equations which define a series of shape invariant potentials which repeats after a cycle of $p$ iterations. These cyclic shape invariant potentials enlarge the limited…
A geometric picture of conformally invariant mechanics is presented. Although the standard form of the model is recovered, the careful analysis of global geometry of phase space leads to the conclusion that, in the attractive case, the…
Using the method of shape invariant potentials, a number of exact solutions of one dimensional effective mass Schrodinger equation are obtained. The solutions with equi-spaced spectrum are discussed in detail.
We study the relationship of the spectral form factor with quantum as well as classical probabilities to return. Defining a quantum return probability in phase space as a trace over the propagator of the Wigner function allows us to…
A quantization procedure, which has recently been introduced for the analysis of Painlev\'e equations, is applied to a general time-independent potential of a Newton equation. This analysis shows that the quantization procedure preserves…