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Related Experiment Video

Updated: Jun 19, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Fractional-time quantum dynamics.

Alexander Iomin¹

¹Department of Physics, Technion, Haifa 32000, Israel.

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

|October 2, 2009

Summary

This summary is machine-generated.

This study applies fractional calculus to quantum dynamics using a fractional time Schrödinger equation. For a specific fractional order (alpha=1/2), the equation becomes isospectral to a comb model, yielding analytical Green's functions.

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Area of Science:

Quantum Mechanics
Fractional Calculus
Mathematical Physics

Background:

Standard quantum dynamics are described by the time-dependent Schrödinger equation.
Fractional calculus offers alternative mathematical frameworks for describing complex systems.

Purpose of the Study:

To explore the application of fractional calculus to quantum processes.
To investigate quantum dynamics using a fractional time Schrödinger equation.

Main Methods:

Utilizing the fractional time Schrödinger equation with a fractional time derivative.
Analyzing the case where the fractional order alpha equals 1/2.
Deriving analytical expressions for Green's functions.

Main Results:

The fractional Schrödinger equation for alpha=1/2 is shown to be isospectral to a comb model.
Analytical expressions for the Green's functions of the considered quantum systems were obtained.
The semiclassical limit of the fractional quantum dynamics was discussed.

Conclusions:

Fractional calculus provides a viable framework for extending quantum dynamics.
The fractional Schrödinger equation exhibits unique properties, such as isospectrality with specific models.
The obtained Green's functions and semiclassical analysis offer insights into fractional quantum systems.