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

Linear time-invariant Systems

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...

Equilibrium Conditions for a Particle

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...

Partial Differential Equations

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...

Quadratic Equations in the Complex Number System

Quadratic Equations in the Complex Number System

A quadratic equation in the form ax2+bx+c=0 can have solutions that vary in nature depending on the value of the discriminant, b2−4ac. In this expression, a is the coefficient of the quadratic term x2, b is the coefficient of the linear term x, and c is the constant term. When the discriminant is negative, the equation has no real number solutions. However, by introducing complex numbers through the imaginary unit i, defined by i=-1, these equations can still be solved.The square root of a...

BIBO stability of continuous and discrete -time systems

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.

Transmission-Line Differential Equations

Transmission-Line Differential Equations

Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from the...

You might also read

Related Articles

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

Sort by

Same author

Assisted chanting and Buddhist end-of-life care in contemporary China.

Palliative & supportive care·2026

Same author

Broadband Photodetector Based on Monolayer MoS<sub>2</sub> Hybridized with Eco-Friendly CuInS<sub>2</sub> Quantum Dots for Weak-to-Strong Light Detection.

ACS applied materials & interfaces·2026

Same author

Docosahexaenoic acid alleviates Ornidazole toxicity related to spermatogenic dysfunction by modulating PPARγ-dependent ER-mitochondrial uncoupling.

Science China. Life sciences·2026

Same author

Intraperitoneal ZP123 improves aged oocyte quality by restoring granulosa cell gap junctions and improving mitochondrial function.

Journal of ovarian research·2026

Same author

Recyclable Cs<sub>2</sub>AgBiBr<sub>6</sub> for Photocatalytic Synthesis of Cyanomethylated Oxindoles.

The Journal of organic chemistry·2026

Same author

The effect of preemptive intravenous paracetamol-mannitol on postoperative analgesia and quality of recovery in elderly patients undergoing total hip arthroplasty.

BMC anesthesiology·2026

Search research articles

Related Experiment Video

Updated: Jul 16, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Polynomial scheme for time evolution of open and closed quantum systems.

Jun Jing¹, H R Ma

¹Institute of Theoretical Physics, Shanghai Jiao Tong University, 800 DongChuan Road, MinHang, Shanghai 200240, China. jingjun@sjtu.edu.cn

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

|March 16, 2007

Summary

We introduce a new Laguerre polynomial expansion for solving the time-dependent Schrödinger equation. This method matches Chebyshev polynomial accuracy and efficiency without Hamiltonian scaling, offering broader applicability.

Related Experiment Videos

Last Updated: Jul 16, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum mechanics
Computational physics
Applied mathematics

Background:

The time-dependent Schrödinger equation governs quantum system evolution.
Accurate numerical methods are crucial for solving this equation.
Existing methods like Chebyshev expansion have limitations.

Purpose of the Study:

To develop a novel numerical scheme for the time-dependent Schrödinger equation.
To leverage Laguerre polynomials for enhanced computational efficiency and accuracy.
To overcome limitations of existing expansion methods.

Main Methods:

Utilizing the generating function of Laguerre polynomials.
Developing a Laguerre polynomial expansion scheme.
Performing theoretical analysis and numerical simulations.
Comparing performance against the Chebyshev polynomial expansion method.

Main Results:

The proposed Laguerre polynomial method demonstrates comparable efficiency and accuracy to the Chebyshev method.
The Laguerre method eliminates the need for Hamiltonian scaling.
The scheme exhibits wider suitability for diverse quantum problems.

Conclusions:

Laguerre polynomial expansion offers a robust and efficient alternative for time-dependent Schrödinger equation calculations.
The method's advantages include no requirement for Hamiltonian scaling and broader applicability.
This approach advances numerical solutions in quantum mechanics.