Related papers: Scale invariant quantum potential leading to globa…
Using the Madelung fluid picture of Schr\"odinger equation for a single free particle moving in one spatial dimension, we shall specify a class of wave functions whose quantum probability density is being trapped by the quantum potential it…
We consider spatially two dimensional Madelung fluid whose irrotational motion reduces into the Schr\"odinger equation for a single free particle. In this respect, we regard the former as a direct generalization of the latter, allowing a…
We develop the most probable wave functions for a single free quantum particle given its momentum and energy by imposing its quantum probability density to maximize Shannon information entropy. We show that there is a class of solutions in…
It has recently been shown that relativistic quantum theory leads to a local interpretation of quantum mechanics wherein the universal wavefunction in configuration space is entirely replaced with an ensemble of local fluid equations in…
In single-particle Madelung mechanics, the single-particle quantum state $\Psi(\vec{x},t) = R(\vec{x},t) e^{iS(\vec{x},t)/\hbar}$ is interpreted as comprising an entire conserved fluid of classical point particles, with local density…
It is demonstrated that the probability density function, given by the square of a quantum mechanical wavefunction that is a real-valued eigenvector of a time-independent, one-body Schroedinger equation, satisfies a compressible-flow…
Starting from relativistic mass-less Madelung fluid, we shall develop a class of typical wave functions by imposing it to maximize Shannon entropy given its finite average quantum potential. We show that there is a class of solutions in…
Quantum many-body states that frequently appear in physics often obey an entropy scaling law, meaning that an entanglement entropy of a subsystem can be expressed as a sum of terms that scale linearly with its volume and area, plus a…
We discuss two-dimensional Madelung fluid dynamics whose irrotational case reduces into the Schr\"odinger equation for a free single particle. We show that the self-trapped spinning-stationary Madelung fluid reported in the previous paper…
It was recently shown that tunneling wavefunction proposal is consistent with loop quantum geometry corrections including both holonomy and inverse scale factor corrections in the gravitational part of a spatially closed isotropic model…
We develop a class of soliton solution of {\it linear} Schr\"odinger equation without external potential. The quantum probability density generates its own boundary inside which there is internal vibration whose wave number is determined by…
More recently, we have proposed a set of noncommutative space that describes the quantum gravity at the Planck scale [J. Phys. A: Math. Theor. 53, 115303 (2020)]. The interesting significant result we found is that, the generalized…
Singularity of the potential function makes quantum tunneling problem mathematically underdetermined. To circumvent the difficulties it introduced in physics, a potential singularity cutoff is often used, followed by a reverse limit…
We consider a non relativistic charged particle in a 1-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time depending electric field. It is represented by a complex…
We investigate a one-dimensional quantum system with a self-similar arrangement of delta-function potential barriers, exhibiting discrete scale invariance. The singular potential induces kinematically enforced symmetry breaking at $x=0$,…
We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the…
In this short paper, we show how a quantum nonlocal effect of far-apart wavepackets in the Schrodinger picture of wavefunctions is replaced by a local instability problem when considering the hydrodynamical formulation of quantum mechanics,…
This article examines the suggestion made in Ref. [EPL, 115 (2016) 60001] that a solution to a particle in an infinite spherical well model, if it is square-integrable, is a physically valid solution, even if at the precise location of the…
The changes that quantum states undergo during measurement are both probabilistic and nonlocal. These two characteristics complement one another to insure compatibility with relativity and maintain conservation laws. The probabilistic…
Is wave function collapse a prediction of the Schr\"odinger equation? This unusual problem is explored in an enlarged framework of interpretation, where quantum dynamics is considered exact and its interpretation is extended to include…