Related papers: Ma-Xu quantization rule and exact WKB condition fo…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
A new method is proposed to calculate wave functions in $k_T$-factorization in \cite{LiMi} as a comment about our paper \cite{FMW}. We point out that the results obtained with the method are in conflict with the translation invariance and…
Exactly solvable potentials of nonrelativistic quantum mechanics are known to be shape invariant. For these potentials, eigenvalues and eigenvectors can be derived using well known methods of supersymmetric quantum mechanics. The majority…
We consider sampling from a Gibbs distribution by evolving finitely many particles. We propose a preconditioned version of a recently proposed noise-free sampling method, governed by approximating the score function with the numerically…
We propose a new variant of the semiclassical quantisation with two independent parameters. The first one is proportional to the Planck constant as usually and the second one is connected with a deviation of the given potential from a very…
Rules of quantization and equations of motion for a finite-dimensional formulation of Quantum Field Theory are proposed which fulfill the following properties: a) both the rules of quantization and the equations of motion are covariant; b)…
The quantization of the gravitational field is discussed within the exact uncertainty approach. The method may be described as a Hamilton-Jacobi quantization of gravity. It differs from previous approaches that take the classical…
We perform a systematic WKB expansion to all orders for a one--dimensional system with potential $V(x)=U_0/\cos^2{(\alpha x)}$. We are able to sum the series to the exact energy spectrum. Then we show that any finite order WKB approximation…
We consider a one-dimensional system of interacting particles, in which particles are subjected to a bistable potential the double-well shape of which is tunable via a shape deformability parameter. Our objective is to examine the impact of…
Fast quantum data transmission faces several shortcomings such as the indistinguishability of some partly overlapping signals, the channel noises, and so on. Based on the encoded quantum data transmission protocol, an unconventional scheme…
Using convex optimization, we propose entanglement-assisted quantum error correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves…
We explore the applicability of the exact renormalization group to the study of tunnelling phenomena. We investigate quantum-mechanical systems whose energy eigenstates are affected significantly by tunnelling through a barrier in the…
An algebraic treatment of shape-invariant potentials is discussed. By introducing an operator which reparametrizes wavefunctions, the shape-invariance condition can be related to a generalized Heisenberg- Weyl algebra. It is shown that this…
An elementary introduction is given to the subject of Supersymmetry in Quantum Mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct new exactly solvable n…
We present an improved analytic parametrisation of the complex in-medium heavy quark potential derived rigorously from the generalised Gauss law. To this end we combine in a self-consistent manner a non-perturbative vacuum potential with a…
We concur with de Castro's observation that the gauge considerations of our approach are not valid. Nevertheless, except for an error that will be corrected, all of our findings are accurate independent of those considerations.
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.
Rule-based classification models described in the language of logic directly predict boolean values, rather than modeling a probability and translating it into a prediction as done in statistical models. The vast majority of existing…
We present a quantum error correcting code that is invariant under the conditional time evolution between spontaneous emissions and which can correct for one general error. The code presented here generalizes previous error correction codes…
In relativistic potential model of heavy-light mesons it is essential to incorporate the chiral radiative corrections before comparing the model predictions with data. Once the radiative corrections are taken into account the potential…