Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Graphing the Wave Function01:13

Graphing the Wave Function

2.1K
Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
2.1K
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

42.9K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
42.9K
Equations of Wave Motion01:02

Equations of Wave Motion

6.0K
Mathematically, the motion of a wave can be studied using a wavefunction. Consider a string oscillating up and down in simple harmonic motion, having a period T. The wave on the string is sinusoidal and is translated in the positive x-direction as time progresses. Sine is a function of the angle θ, oscillating between +A and −A and repeating every 2π radians. To construct a wave model, the ratio of the angle θ and the position x is considered.
6.0K
The de Broglie Wavelength02:32

The de Broglie Wavelength

26.2K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
26.2K
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

120
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
120
Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

191
The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx  and a shunt capacitance CΔx.
191

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

S-Pen Technology and Online Signatures: Cross-Device Variability and Its Implications for Mobile Biometric Authentication.

Sensors (Basel, Switzerland)·2026
Same author

A three-dimensional memristor-based hyperchaotic map for pseudorandom number generation and multi-image encryption.

Chaos (Woodbury, N.Y.)·2025
Same author

An Effective and Fast Model for Characterization of Cardiac Arrhythmia and Congestive Heart Failure.

Diagnostics (Basel, Switzerland)·2025
Same author

Enhanced Control of Nonlinear Systems Under Control Input Constraints and Faults: A Neural Network-Based Integral Fuzzy Sliding Mode Approach.

Entropy (Basel, Switzerland)·2025
Same author

The dynamical behavior effects of different numbers of discrete memristive synaptic coupled neurons.

Cognitive neurodynamics·2024
Same author

Conduction and validation of a novel prognostic signature in cervical cancer based on the necroptosis characteristic genes via integrating of multiomics data.

Computers in biology and medicine·2023

Related Experiment Video

Updated: Aug 30, 2025

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

8.8K

Laguerre Wavelet Approach for a Two-Dimensional Time-Space Fractional Schrödinger Equation.

Stelios Bekiros1,2,3, Samaneh Soradi-Zeid4, Jun Mou5

  • 1FEMA, University of Malta, MSD 2080 Msida, Malta.

Entropy (Basel, Switzerland)
|August 26, 2022
PubMed
Summary
This summary is machine-generated.

This study presents a new numerical method for solving the two-dimensional time-space fractional Schrödinger equation. The Laguerre wavelet approach combined with collocation provides highly accurate solutions for this complex mathematical problem.

Keywords:
Laguerre waveletSchrödinger equationfractional derivativetwo-dimensional fractional equation

More Related Videos

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.7K
Recording Spatially Restricted Oscillations in the Hippocampus of Behaving Mice
07:10

Recording Spatially Restricted Oscillations in the Hippocampus of Behaving Mice

Published on: July 1, 2018

8.9K

Related Experiment Videos

Last Updated: Aug 30, 2025

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
08:54

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

Published on: February 13, 2018

8.8K
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

11.7K
Recording Spatially Restricted Oscillations in the Hippocampus of Behaving Mice
07:10

Recording Spatially Restricted Oscillations in the Hippocampus of Behaving Mice

Published on: July 1, 2018

8.9K

Area of Science:

  • Numerical analysis
  • Mathematical physics
  • Quantum mechanics

Background:

  • The fractional Schrödinger equation is a key model in quantum mechanics and nonlinear optics.
  • Developing accurate numerical solutions for fractional differential equations is computationally challenging.
  • Existing methods may lack efficiency or precision for two-dimensional time-space fractional problems.

Purpose of the Study:

  • To determine accurate numerical solutions for the two-dimensional time-space fractional Schrödinger equation.
  • To introduce and validate the Laguerre wavelet approach for this specific problem.
  • To demonstrate the efficacy of a collocation method for solving the resulting discretized nonlinear system.

Main Methods:

  • Laguerre wavelet approach for discretization.
  • Collocation method for solving the nonlinear system.
  • Numerical determination of unknown parameters.

Main Results:

  • The Laguerre wavelet approach effectively discretizes the fractional Schrödinger equation.
  • The collocation method efficiently solves the nonlinear discretized problem.
  • Numerical examples confirm the high accuracy of the proposed method.

Conclusions:

  • The combined Laguerre wavelet and collocation method is a powerful tool for solving the two-dimensional time-space fractional Schrödinger equation.
  • The approach offers a significant improvement in accuracy for fractional differential equations.
  • This method provides a reliable framework for future research in fractional dynamics.