Related papers: Schrodinger Equation As a General Optimization Alg…
This paper presents a global optimization approach to quantum mechanics, which describes the most fundamental dynamics of the universe. It suggests that the wave-like behavior of (sub)atomic particles could be the critical characteristic of…
The Schrodinger equation is one of the most important equations in physics and chemistry and can be solved in the simplest cases by computer numerical methods. Since the beginning of the 70s of the last century the computer began to be used…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
It is shown that the Schrodinger equation is a byproduct of more deterministic Boltzmann-like equation. All physical information is derived from the solution of this equation, which is a function of space and momentum. The additional terms…
Quantum mechanics take the sum of first finite order approximate solutions of time-dependent perturbation to substitute the exact solution. From the point of mathematics, it may be correct only in the convergent region of the time-dependent…
Quantum mechanics is one of the basic theories of modern physics. Here, the famous Schr\"odinger equation and the differential operators representing mechanical quantities in quantum mechanics are derived, just based on the principle that…
The belief propagation algorithm has been recognized in the information theory community as a soft-decision iterative decoding algorithm. It is the most powerful algorithm found so far for attacking hard optimization problems in channel…
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…
Any time-dependent solution of Schr\"{o}dinger equation may be always correlated to a solution of Hamilton equations or to a statistical combination of their solutions; only the set of corresponding solutions is somewhat smaller (due to…
In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…
Statistical and stochastic analysis based on thermodynamics has been the main analysis framework for stochastic global optimization. Recently, appearing quantum annealing or quantum tunneling algorithm for global optimization, we require a…
The Schrodinger equation has been considered to be a postulate of quantum physics, but it is also perceived and derived heuristically as the quantum equivalent of the classical energy relation. We indicate that the Schrodinger equation…
It is argued that the Schr\"odinger equation does not yield a correct description of the quantum-mechanical time evolution of states of isolated (open) systems featuring events. A precise general law for the time evolution of states…
The Schrodinger equation based on the de Broglie wave is the most fundamental equation of the quantum mechanics. There can be no doubt about it's prediction validity. However, the probabilistic interpretation on the quantum mechanics has…
The conventional, time-dependent Schroedinger equation describes only unidirectional time evolution of the state of a physical system, i.e., forward or, less commonly, backward. This paper proposes a generalized quantum dynamics for the…
An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the…
A central aim of physics is to describe the dynamics of physical systems. Schrodinger's equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most…
Using classical statistics, Schrodinger equation in quantum mechanics is derived from complex space model. Phase-space probability amplitude, that can be defined on classical point of view, has connections to probability amplitude in…
Using the simplest but fundamental example, the problem of the infinite potential well, this paper makes an ideological attempt (supported by rigorous mathematical proofs) to approach the issue of…
We develop a quantum algorithm for solving high-dimensional time-fractional heat equations. By applying the dimension extension technique from [FKW23], the $d+1$-dimensional time-fractional equation is reformulated as a local partial…