scholarly journals Nonadiabatic rotational states of the hydrogen molecule

2018 ◽  
Vol 20 (1) ◽  
pp. 247-255 ◽  
Author(s):  
Krzysztof Pachucki ◽  
Jacek Komasa
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Hydrogen Molecule ◽  
High Accuracy ◽  
Wave Functions ◽  
New Method ◽  
Body System ◽  
Coulomb Interactions ◽  
Rotational States

A new method of solving the Schrödinger equation to a high accuracy for a four-body system with Coulomb interactions using exponential wave functions.

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 TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

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.

scholarly journals A new method for the solution of the Schrödinger equation

2004 ◽  
Vol 37 (10) ◽  
pp. 3515-3525 ◽  
Author(s):  
Paolo Amore ◽  
Alfredo Aranda ◽  
Arturo De Pace
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
New Method

A NEW NUMEROV-TYPE METHOD FOR COMPUTING EIGENVALUES AND RESONANCES OF THE RADIAL SCHRÖDINGER EQUATION

1996 ◽  
Vol 07 (01) ◽  
pp. 33-41 ◽  
Author(s):  
T. E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Results ◽  
New Method ◽  
Resonance Problem ◽  
Step Method ◽  
Type Method ◽  
Radial Schrödinger Equation ◽  
Better Than

A two-step method is developed for computing eigenvalues and resonances of the radial Schrödinger equation. Numerical results obtained for the integration of the eigenvalue and the resonance problem for several potentials show that this new method is better than other similar methods.

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