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Quantum Numbers

Quantum Numbers

It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

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.

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

The de Broglie Wavelength

The de Broglie Wavelength

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...

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...

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Related Experiment Video

Updated: Oct 4, 2025

Uncovering Hidden Dynamics of Natural Photonic Structures Using Holographic Imaging

Uncovering Hidden Dynamics of Natural Photonic Structures Using Holographic Imaging

Published on: March 31, 2022

Quantum information in holographic duality.

Bowen Chen¹, Bartłomiej Czech¹, Zi-Zhi Wang¹

¹Institute for Advanced Study, Tsinghua University, Beijing 100084, People's Republic of China.

Reports on Progress in Physics. Physical Society (Great Britain)

|February 3, 2022

Summary

This summary is machine-generated.

Quantum information theory concepts explain gravity in the anti-de Sitter/conformal field theory correspondence. This review covers black hole thermodynamics, holographic duality, and entanglement entropy for new researchers.

Keywords:

AdS/CFT correspondence black holes emergent spacetime entanglement entropy holographic duality quantum information theory tensor networks

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Last Updated: Oct 4, 2025

Uncovering Hidden Dynamics of Natural Photonic Structures Using Holographic Imaging

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Published on: March 31, 2022

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Published on: June 8, 2018

Area of Science:

Theoretical Physics
Quantum Information Theory
Quantum Gravity

Background:

Black hole thermodynamics provides foundational principles.
Holographic duality connects quantum field theories and gravitational theories.
Quantum information concepts are crucial for understanding the gravitational bulk.

Purpose of the Study:

To provide a pedagogical review of quantum information theory's role in the anti-de Sitter/conformal field theory correspondence.
To equip researchers with sufficient knowledge to initiate original projects in this field.
To bridge the gap between quantum mechanics/general relativity and advanced holographic concepts.

Main Methods:

Introduction to the Ryu-Takayanagi proposal and the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) relation.
Utilizing tensor networks for visualizing holographic entanglement.
Discussion of modern concepts: Rényi entropies, replica trick, kinematic space, modular Berry phases, entanglement wedge cross-sections, and bit threads.

Main Results:

Demonstration of how boundary entanglement entropies constrain bulk geometries.
Analysis of fundamental relations like the monogamy of mutual information.
Exploration of black hole physics, including holographic complexity and the information paradox.

Conclusions:

Quantum information theory offers a powerful framework for understanding quantum gravity and the AdS/CFT correspondence.
Entanglement properties on the boundary dictate the structure of the gravitational bulk.
Advanced topics like firewalls, islands, and replica wormholes are illuminated through this lens.