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Quantum Numbers

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Curvilinear Motion: Polar Coordinates

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In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
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Singularity Functions for Shear

Singularity Functions for Shear

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Related Experiment Video

Updated: May 18, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Quantum splines.

Dorje C Brody¹, Darryl D Holm, David M Meier

¹Mathematical Sciences, Brunel University, Uxbridge, United Kingdom.

Physical Review Letters

|September 26, 2012

Summary

This summary is machine-generated.

Researchers developed quantum splines, a method to precisely control quantum states over time by minimizing Hamiltonian changes. This advance offers efficient quantum control for applications like coherent states.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Last Updated: May 18, 2026

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

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
Quantum control theory

Background:

Quantum systems evolve via unitary transformations.
Precise control over quantum states is crucial for quantum technologies.
Existing methods may not be optimal for smooth, time-dependent state evolution.

Purpose of the Study:

To define and solve the quantum spline problem.
To develop an efficient numerical method for computing quantum splines.
To demonstrate the application of quantum splines in controlling quantum states.

Main Methods:

Defining quantum splines as time-parametrized curves in unitary transformation space.
Minimizing the trace norm of the time rate of change of the Hamiltonian.
Developing and implementing a numerical scheme for quantum spline computation.

Main Results:

The solution to the quantum spline problem was obtained.
A numerical scheme for computing quantum splines was developed and implemented.
An example demonstrating quantum control of coherent states using quantum splines was presented.

Conclusions:

Quantum splines provide a novel framework for optimal quantum state control.
The developed method enables efficient and smooth traversal of quantum states.
This technique has potential applications in advancing quantum computing and simulation.