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.

Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

Geometric Mean

Geometric Mean

The mean is a measure of the central tendency of a data set. In some data sets, the data is inherently multiplicative, and the arithmetic mean is not useful. For example, the human population multiplies with time, and so does the credit amount of financial investment, as the interest compounds over successive time intervals.
In cases of multiplicative data, the geometric mean is used for statistical analysis. First, the product of all the elements is taken. Then, if there are n elements in the...

Work Done in an Adiabatic Process

Work Done in an Adiabatic Process

Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position. The temperature, pressure, and volume of the resulting gas-air mixture are 20 °C, 1.00 x 105 N/m2, and 240 cm3 , respectively. The mixture is then compressed adiabatically to a volume of 40 cm3. Note that, in the actual operation of an automobile engine, the compression is not...

Control Volume and System Representations

Control Volume and System Representations

Two key frameworks are employed to analyze mass, energy, and momentum transfer: the control volume approach and the system approach. These frameworks offer different perspectives, depending on whether the focus is on a specific region in space (control volume approach) or a defined mass of fluid (system approach).
The control volume approach considers a stationary region in space through which fluid flows. This region is bounded by a control surface. For instance, in the case of water...

State Space Representation

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

You might also read

Related Articles

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

Sort by

Same author

An implicit split-operator algorithm for the nonlinear time-dependent Schrödinger equation.

The Journal of chemical physics·2021

Same author

High-order geometric integrators for representation-free Ehrenfest dynamics.

The Journal of chemical physics·2021

Same author

Time-reversible and norm-conserving high-order integrators for the nonlinear time-dependent Schrödinger equation: Application to local control theory.

The Journal of chemical physics·2021

Same author

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

The Journal of chemical physics·2021

Same author

Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?

The Journal of chemical physics·2020

Same author

On-the-fly ab initio semiclassical evaluation of third-order response functions for two-dimensional electronic spectroscopy.

The Journal of chemical physics·2020

Search research articles

Related Experiment Video

Updated: Jan 24, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Efficient geometric integrators for nonadiabatic quantum dynamics. I. The adiabatic representation.

Seonghoon Choi¹, Jiří Vaníček¹

¹Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

The Journal of Chemical Physics

|June 3, 2019

Summary

New implicit geometric integrators precisely solve the Schrödinger equation for complex molecular systems. These methods offer enhanced accuracy and efficiency, conserving crucial physical properties for quantum dynamics simulations.

More Related Videos

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Related Experiment Videos

Last Updated: Jan 24, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Area of Science:

Quantum Chemistry
Computational Physics
Theoretical Chemistry

Background:

Geometric integrators for the Schrödinger equation preserve invariants of the exact solution.
The split-operator algorithm is limited to separable Hamiltonians.
Accurate numerical solutions are crucial for understanding quantum dynamics.

Purpose of the Study:

To develop implicit geometric integrators for both separable and nonseparable Hamiltonians.
To apply these integrators to the nonadiabatic molecular Hamiltonian.
To achieve arbitrary order of accuracy in time step for quantum dynamics.

Main Methods:

Combining the dynamic Fourier method with recursive symmetric composition of the trapezoidal rule or implicit midpoint method.
Developing implicit geometric integrators for nonadiabatic molecular Hamiltonians.
Analytical proofs and numerical demonstrations on a two-surface NaI model.

Main Results:

Developed arbitrary-order implicit geometric integrators that are unitary, symplectic, symmetric, time-reversible, and stable.
These integrators conserve energy exactly, unlike the split-operator method.
Achieved a thousand-fold speedup compared to the Crank-Nicolson method for high accuracy (10^-10 wavefunction convergence error).

Conclusions:

The new implicit geometric integrators provide a highly accurate and efficient approach for quantum dynamics simulations.
They overcome the limitations of the split-operator method, applicable to a wider range of Hamiltonians.
These methods are particularly beneficial when high accuracy is required, offering significant computational advantages.