Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Interference and Diffraction02:18

Interference and Diffraction

53.9K
Interference is a characteristic phenomenon exhibited by waves. When two electromagnetic waves interact with their peaks and troughs coinciding, a resulting wave with enhanced amplitude is produced. This is known as constructive interference. In this case, the two waves interacting are in phase with each other.
53.9K
The de Broglie Wavelength02:32

The de Broglie Wavelength

34.4K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
34.4K
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

61.4K
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.
61.4K
Determination of Crystal Structures01:29

Determination of Crystal Structures

58
In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
58
X-ray Crystallography02:18

X-ray Crystallography

26.7K
The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
26.7K
Imperfections in Crystal Structure: Stoichiometric Point Defects01:26

Imperfections in Crystal Structure: Stoichiometric Point Defects

62
Schottky defects arise when some lattice points in a crystal, such as those in NaCl, remain unoccupied, creating lattice vacancies without disturbing the overall electrical neutrality of the crystal. This defect is common in ionic crystals where the positive and negative ions are similar in size, as seen in sodium chloride and cesium chloride. The presence of Schottky defects enables the crystal to conduct electricity to a small extent through an ionic mechanism. Electric fields cause nearby...
62

You might also read

Related Articles

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

Sort by
Same author

Macrophage Membrane-Coated Nanoparticles Alleviate Hepatic Ischemia-Reperfusion Injury Caused by Orthotopic Liver Transplantation by Neutralizing Endotoxin.

International journal of nanomedicine·2020
Same author

Expression Level of Wnt5a Was Related to the Therapeutic Effects of First-Generation EGFR-TKIs.

OncoTargets and therapy·2020
Same author

Anlotinib or platinum-pemetrexed as second-line therapy in EGFR T790M-negative lung cancer.

Annals of palliative medicine·2020
Same author

Measuring health-related quality of life in elementary and secondary school students using the Chinese version of the EQ-5D-Y in rural China.

BMC public health·2020
Same author

Arsenic trioxide potentiates Gilteritinib-induced apoptosis in FLT3-ITD positive leukemic cells via IRE1a-JNK-mediated endoplasmic reticulum stress.

Cancer cell international·2020
Same author

A Grading System for Invasive Pulmonary Adenocarcinoma: A Proposal From the International Association for the Study of Lung Cancer Pathology Committee.

Journal of thoracic oncology : official publication of the International Association for the Study of Lung Cancer·2020

Related Experiment Video

Updated: Mar 22, 2026

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
08:44

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

Published on: August 22, 2017

8.2K

Diffraction-free beams in fractional Schrödinger equation.

Yiqi Zhang1, Hua Zhong1, Milivoj R Belić2

  • 1Key Laboratory for Physical Electronics and Devices of the Ministry of Education &Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an 710049, China.

Scientific Reports
|April 22, 2016
PubMed
Summary

This study explores Gaussian beam propagation in the fractional Schrödinger equation (FSE). Results show beams are diffractionless, splitting or deflecting based on dimensionality and chirp, revealing a novel Talbot effect.

More Related Videos

Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

11.9K
Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
10:39

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Published on: October 11, 2016

10.2K

Related Experiment Videos

Last Updated: Mar 22, 2026

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
08:44

Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene

Published on: August 22, 2017

8.2K
Spatial Separation of Molecular Conformers and Clusters
10:37

Spatial Separation of Molecular Conformers and Clusters

Published on: January 9, 2014

11.9K
Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating
10:39

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating

Published on: October 11, 2016

10.2K

Area of Science:

  • Quantum mechanics
  • Nonlinear optics
  • Mathematical physics

Background:

  • The fractional Schrödinger equation (FSE) describes quantum systems with long-range interactions.
  • Gaussian beams are fundamental solutions in wave propagation studies.
  • Understanding beam dynamics in FSE is crucial for applications in optics and quantum physics.

Purpose of the Study:

  • To analytically and numerically investigate the propagation of 1D and 2D Gaussian beams in the FSE without a potential.
  • To explore the effects of linear chirp on beam trajectories and diffraction properties.
  • To introduce and analyze the Talbot effect for diffractionless beams within the FSE framework.

Main Methods:

  • Analytical solutions for Gaussian beam propagation in FSE.
  • Numerical simulations to verify analytical findings.
  • Mathematical analysis of beam splitting, deflection, and diffraction.

Main Results:

  • 1D Gaussian beams split into two nondiffracting beams without chirp.
  • 2D Gaussian beams exhibit conical diffraction without chirp.
  • Chirped 1D beams deflect along specific trajectories, independent of chirp.
  • Chirped 2D beams deflect along diffraction cones, with direction dependent on chirp.
  • Both 1D and 2D beams demonstrate diffractionless and uniform propagation.
  • The Talbot effect for diffractionless beams in FSE is introduced.

Conclusions:

  • Gaussian beams exhibit unique diffractionless and splitting/deflecting behaviors in the FSE.
  • The study reveals controllable beam steering via chirp in 2D propagation.
  • The findings extend the understanding of wave phenomena in fractional media and introduce a new Talbot effect.