scholarly journals Merits of using density matrices instead of wave functions in the stationary Schrödinger equation for systems with symmetries

2020 ◽  
Vol 53 (7) ◽  
pp. 075301
Author(s):  
E Shpagina ◽  
F Uskov ◽  
N Il’in ◽  
O Lychkovskiy
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Density Matrices ◽  
Stationary Schrödinger Equation

scholarly journals On the method of pseudopotential for Schrödinger equation with nonlocal boundary conditions

2001 ◽  
Vol 6 (6) ◽  
pp. 329-338
Author(s):  
Yuriy Valentinovich Zasorin
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Explicit Form ◽  
Schrodinger Equation ◽  
Scattering Amplitude ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Wave Functions ◽  
Stationary Schrödinger Equation ◽  
Fixed Level

For stationary Schrödinger equation inℝ nwith the finite potential the singular pseudopotential is constructed in the form allowing us to find wave functions. The method does not require the knowledge of the explicit form of a potential and assumes only knowledge of the scattering amplitude for fixed level of energy.

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.

A Student's Guide to the Schrödinger Equation

2020 ◽  
Author(s):  
Daniel A. Fleisch
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Plain Language ◽  
Science And Engineering ◽  
Popular Approach ◽  
Matlab Code ◽  
Mathematical Techniques

Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.

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