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

Real-World Applications of Space Curves

Real-World Applications of Space Curves

Modern aerospace navigation depends on the accurate prediction of motion in three-dimensional space. In defense applications, radar systems continuously track both interceptors and moving aerial targets to find whether their flight paths will result in a collision. These motions are modeled mathematically as space curves, which represent paths that change continuously with time. Each object’s position is described by a vector function that specifies its location in terms of time-dependent...

Curves Defined by Parametric Equations

Curves Defined by Parametric Equations

A baseball hit into the air follows a parabolic trajectory when air resistance is neglected. The motion can be described within a two-dimensional coordinate system, where both the horizontal displacement and vertical height are functions of time. Instead of expressing the trajectory as a single function of position, the motion is modeled using parametric equations: one function for the horizontal position and another for the vertical position as time progresses. Let the horizontal position be...

Orthogonal Trajectories

Orthogonal Trajectories

Orthogonal trajectories describe the geometric relationship between two families of curves that intersect each other at right angles. One illustrative case involves a family of parabolas that open sideways along the x-axis. These curves share a common shape but differ by a scaling parameter, resulting in a set of curves that all pass through the origin and widen at different rates.Determining Orthogonal TrajectoriesTo identify the orthogonal trajectories for these parabolas, the first step...

Kinematic Equations: Problem Solving

Kinematic Equations: Problem Solving

When analyzing one-dimensional motion with constant acceleration, the problem-solving strategy involves identifying the known quantities and choosing the appropriate kinematic equations to solve for the unknowns. Either one or two kinematic equations are needed to solve for the unknowns, depending on the known and unknown quantities. Generally, the number of equations required is the same as the number of unknown quantities in the given example. Two-body pursuit problems always require two...

Kinematic Equations - II

Kinematic Equations - II

The second kinematic equation expresses the final position of an object in terms of its initial position, the distance traveled with the initial constant velocity, and the distance traveled due to a change in velocity. Similar to the first kinematic equation, this equation is also only valid when the acceleration is constant throughout the motion of an object.
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...

Kinematic Equations - III

Kinematic Equations - III

The first two kinematic equations have time as a variable, but the third kinematic equation is independent of time. This equation expresses final velocity as a function of the acceleration and distance over which it acts. The fourth kinematic equation does not have an acceleration term and provides the final position of the object at time t in terms of the initial and final velocities. This equation is useful when the value of the constant acceleration is unknown.
Using the kinematic equations,...

You might also read

Related Articles

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

Sort by

Same author

Generalized kicked rotor: Periodic forcing with finite-width pulses and the role of shifting the kick.

Physical review. E·2026

Same author

The robustness of composite pulses elucidated by classical mechanics: stability around the globe.

Physical chemistry chemical physics : PCCP·2025

Same author

The geometry of the classical action in phase space.

The Journal of chemical physics·2025

Same author

Exploring the role of chaos in model recollision processes.

The Journal of chemical physics·2025

Same author

Control of concerted back-to-back double ionization dynamics in helium.

The Journal of chemical physics·2021

Same author

Communication: Systematic elimination of Stokes divergences emanating from complex phase space caustics.

The Journal of chemical physics·2018

Same journal

A data-driven modeling study on the accurate identification of Doppler-free saturated absorption spectra in diatomic tellurium (130Te2).

The Journal of chemical physics·2026

Same journal

Anharmonic phonons via quantum thermal bath simulations.

The Journal of chemical physics·2026

Same journal

Quantum simulation of alignment dependent differential cross sections in co-propagating molecular beams at cold collision energies.

The Journal of chemical physics·2026

Same journal

Non-additive ion effects on the coil-globule equilibrium of a generic polymer in aqueous salt solutions.

The Journal of chemical physics·2026

Same journal

Insights into the unexpected small reduction of the temperature of maximum density of water by lithium chloride addition.

The Journal of chemical physics·2026

Same journal

Optical frequency comb double-resonance spectroscopy of the 9030-9175 cm-1 states of ethylene.

The Journal of chemical physics·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 5, 2026

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

Complex trajectory method in time-dependent WKB.

Yair Goldfarb¹, Jeremy Schiff, David J Tannor

¹Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 76100, Israel.

The Journal of Chemical Physics

|May 2, 2008

Summary

This summary is machine-generated.

This study enhances the complex time-dependent WKB method by superposing trajectories and incorporating higher-order terms. These improvements overcome limitations in quantum mechanical simulations, offering a competitive semiclassical alternative.

More Related Videos

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Related Experiment Videos

Last Updated: Jul 5, 2026

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Trajectory Data Analyses for Pedestrian Space-time Activity Study

Published on: February 25, 2013

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

Area of Science:

Quantum mechanics
Computational chemistry
Theoretical physics

Background:

The complex time-dependent WKB (CWKB) formulation offers a semiclassical approach to quantum mechanical problems.
Existing CWKB methods show limitations with wavefunctions exhibiting interference, such as oscillations and nodes.

Purpose of the Study:

To significantly improve the CWKB formulation by addressing its limitations.
To enhance the accuracy and applicability of semiclassical methods in quantum dynamics.

Main Methods:

Superposing contributions from crossing trajectories to handle wavefunctions with interference.
Incorporating higher-order terms in the WKB expansion for improved approximation.
Implementing equations of motion for caustics and Stokes lines to manage discontinuities.

Main Results:

The improved CWKB method successfully overcomes limitations related to wavefunction interference.
Inclusion of higher-order terms demonstrably enhances the approximation accuracy.
The implementation of caustics and Stokes line dynamics addresses Stokes discontinuities.

Conclusions:

The enhanced CWKB formulation provides a more robust and accurate semiclassical alternative.
These advancements make the CWKB method a competitive option for time-dependent quantum simulations.
The study paves the way for broader applications of semiclassical methods in complex systems.