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We derive possible corrections to the statistical predictions of quantum mechanics in measurement over ensemble of identically prepared system based on a hidden variable model of quantization developed in the previous work. The corrections…
In this paper we address the problem of a particle moving in singular one dimensional potentials in the framework of quantum mechanics with minimal length. Using the momentum space representation we solve exactly the Schrodinger equation…
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…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
We rederive uncertainty relations for the angular position and momentum of a particle on a circle by employing the exponential of the angle instead of the angle itself, which leads to circular variance as a natural measure of resolution.…
In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the Past Hypothesis) to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to…
In this paper, we develop a new approach to investigation of the uniform stability for inverse spectral problems. We consider the non-self-adjoint Sturm-Liouville problem that consists in the recovery of the potential and the parameters of…
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…
The Heisenberg uncertainty relation is known to be obtainable by a purely mathematical argument. Based on that fact, here it is shown that the Heisenberg uncertainty relation remains valid when Quantum Mechanics is re-formulated within far…
In this paper we generalize the concept of Wigner function in the case of quantum mechanics with a minimum length scale arising due to the application of a generalized uncertainty principle (GUP). We present the phase space formulation of…
We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the…
A reference potential approach to the one-dimensional quantum-mechanical inverse problem is developed. All spectral characteristics of the system, including its discrete energy spectrum, the full energy dependence of the phase shift, and…
A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…
We study an internal structure of (2+1)-dimensional black hole with the neutral scalar matter in the spherically symmetric geometry by using a quantum theory of gravity which holds in the both vicinities of the singularity and the apparent…
We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is…
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is employed to address the hitherto nonrenormalizable gravitational interaction following which the…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
In this paper we propose a quantum algorithm to determine the Tikhonov regularization parameter and solve the ill-conditioned linear equations, for example, arising from the finite element discretization of linear or nonlinear inverse…
We revisit the Extended Uncertainty Principle (EUP) from an operational viewpoint, replacing wavefunction-based widths with apparatus-defined position constraints such as a finite slit of width $\Delta x$ or a geodesic ball of radius $R$.…