Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

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. Schrödinger...

Graphing the Wave Function

Graphing the Wave Function

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.

Properties of Laplace Transform-II

Properties of Laplace Transform-II

Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
Time differentiation involves analyzing the rate of change of a function over time. Mathematically, it is the derivative of a function with respect to time. This concept can be likened to tracking...

Discrete-Time Fourier Series

Discrete-Time Fourier Series

The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...

The de Broglie Wavelength

The de Broglie Wavelength

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...

Equations of Wave Motion

Equations of Wave Motion

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.

You might also read

Related Articles

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

Sort by

Same author

Quantum-Electrodynamical Time-Dependent Density Functional Theory Description of Molecules in Optical Cavities.

Journal of chemical theory and computation·2026

Same author

Time-dependent density functional theory investigation of the formation of H3+ from alkanes.

The Journal of chemical physics·2025

Same author

Time-dependent density-functional study of intermolecular Coulombic decay for 2a1 ionized water dimer.

The Journal of chemical physics·2025

Same author

CH(A) Radical Formation in Coulomb Explosion from Butane Seeded Plasma Generated with Chirp-Controlled Ultrashort Laser Pulses.

ACS omega·2025

Same author

Erratum: "Real-space, real-time approach to quantum-electrodynamical time-dependent density functional theory" [J. Chem. Phys. 157, 194106 (2022)].

The Journal of chemical physics·2023

Same author

Real-space, real-time approach to quantum-electrodynamical time-dependent density functional theory.

The Journal of chemical physics·2022

Search research articles

Related Experiment Video

Updated: May 24, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Solution of the time-dependent Schrödinger equation using time-dependent basis functions.

Kálmán Varga¹

¹Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 10, 2012

Summary

This study introduces an efficient time-dependent basis method for solving the Schrödinger equation, enabling accurate wave function propagation. The approach accurately models atomic ionization and molecular absorption spectra.

More Related Videos

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Related Experiment Videos

Last Updated: May 24, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Area of Science:

Quantum mechanics
Computational chemistry
Atomic and molecular physics

Background:

Solving the time-dependent Schrödinger equation is crucial for understanding quantum dynamics.
Traditional methods often face challenges with computational efficiency and accuracy in time propagation.

Purpose of the Study:

To develop and demonstrate an efficient method for solving the time-dependent Schrödinger equation.
To enable reflection-free time propagation of quantum wave functions.

Main Methods:

Utilized an explicitly time-dependent basis set for solving the Schrödinger equation.
Applied the method to simulate time-dependent quantum phenomena.

Main Results:

Achieved efficient and reflection-free time propagation of the wave function.
Successfully calculated above-threshold ionization of a model atom.
Determined the optical absorption spectrum of a sodium dimer.

Conclusions:

The explicitly time-dependent basis approach is a powerful tool for quantum dynamics simulations.
The method offers a robust and accurate way to study atomic and molecular properties under time-dependent perturbations.