Parallel Computing Algorithm and Visualization of Particles wave Functions in a Quantum System

2021 ◽  
Author(s):  
Bogdan Sus ◽  
Sergiy Zagorodnyuk ◽  
Oleksandr Bauzha ◽  
Alla Ivanyshyn
Keyword(s):  
Parallel Computing ◽  
Quantum System ◽  
Wave Functions ◽  
Computing Algorithm

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

Exact solutions of a quartic potential

2019 ◽  
Vol 34 (26) ◽  
pp. 1950208 ◽  
Author(s):  
Qian Dong ◽  
Guo-Hua Sun ◽  
M. Avila Aoki ◽  
Chang-Yuan Chen ◽  
Shi-Hai Dong
Keyword(s):  
Exact Solutions ◽  
Quantum System ◽  
Analytical Solutions ◽  
Wave Functions ◽  
Negative Potential ◽  
Potential Parameter ◽  
Real Numbers ◽  
Quartic Potential ◽  
Heun Functions ◽  
Potential Parameters

We find that the analytical solutions to quantum system with a quartic potential [Formula: see text] (arbitrary [Formula: see text] and [Formula: see text] are real numbers) are given by the triconfluent Heun functions [Formula: see text]. The properties of the wave functions, which are strongly relevant for the potential parameters [Formula: see text] and [Formula: see text], are illustrated. It is shown that the wave functions are shrunk to the origin for a given [Formula: see text] when the potential parameter [Formula: see text] increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter [Formula: see text] increases or parameter [Formula: see text] decreases for a given negative potential parameter [Formula: see text]. The minimum value of the double well case ([Formula: see text]) is given by [Formula: see text] at [Formula: see text].

A New Parallel Computing Algorithm to Get the Cubic Subgraph for a Simple Graph

2015 ◽  
Vol 12 (10) ◽  
pp. 3006-3008
Author(s):  
Zuwen Ji ◽  
Wenhong Cao ◽  
Zhaocai Wang ◽  
Yufang Qin ◽  
Lei Li
Keyword(s):  
Parallel Computing ◽  
Simple Graph ◽  
Computing Algorithm

Numerical Solution of 2-D Water Entry Problems Based on a CIP Method and a Parallel Computing Algorithm

2015 ◽  
Author(s):  
Peng Wen ◽  
Wei Qiu
Keyword(s):  
Parallel Computing ◽  
Message Passing ◽  
Message Passing Interface ◽  
Water Entry ◽  
Navier Stokes ◽  
Cip Method ◽  
Constrained Interpolation ◽  
Decomposition Scheme ◽  
Computing Algorithm ◽  
Speed Up

A constrained interpolation profile (CIP) method has been developed to solve 2-D water entry problems. This paper presents the further development of the numerical method using staggered grids and a parallel computing algorithm. In this work, the multi-phase slamming problems, governed by the Navier-Stokes (N-S) equations, are solved by a CIP-based finite difference method. The interfaces between different phases (solid, water and air) are captured using density functions. A parallel computing algorithm based on the Message Passing Interface (MPI) method and the domain decomposition scheme was implemented to speed up the computations. The effect of decomposition scheme on the solution and the speed-up were studied. Validation studies were carried out for the water entry of various 2-D wedges and a ship section. The predicted slamming force, pressure distribution and free surface elevation are compared with experimental results and other numerical results.

Quantum system: Wave function, entanglement and the uncertainty principle

2021 ◽  
pp. 2150222 ◽  
Author(s):  
A. V. Melkikh
Keyword(s):  
Wave Function ◽  
Quantum System ◽  
Uncertainty Principle ◽  
Wave Functions ◽  
Identical Particles ◽  
Quantum Particles ◽  
System Of Particles ◽  
Definition Of

A definition of entanglement based on the overlap of wave functions of identical particles is proposed. A definition of a quantum system of particles related to their entanglement with each other and the environment is proposed. It is shown that in the general case, the uncertainty principle cannot be formulated for a system of quantum particles in the form of a single inequality.

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