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Related Concept Videos

The Quantum-Mechanical Model of an Atom02:45

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. Schrödinger...
The Bohr Model02:18

The Bohr Model

Following the work of Ernest Rutherford and his colleagues in the early twentieth century, the picture of atoms consisting of tiny dense nuclei surrounded by lighter and even tinier electrons continually moving about the nucleus was well established. This picture was called the planetary model since it pictured the atom as a miniature “solar system” with the electrons orbiting the nucleus like planets orbiting the sun. The simplest atom is hydrogen, consisting of a single proton as the nucleus...
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
Molecular Orbital Theory I02:35

Molecular Orbital Theory I

Overview of Molecular Orbital Theory
The Energies of Atomic Orbitals03:21

The Energies of Atomic Orbitals

In an atom, the negatively charged electrons are attracted to the positively charged nucleus. In a multielectron atom, electron-electron repulsions are also observed. The attractive and repulsive forces are dependent on the distance between the particles, as well as the sign and magnitude of the charges on the individual particles. When the charges on the particles are opposite, they attract each other. If both particles have the same charge, they repel each other.

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Related Experiment Video

Updated: May 21, 2026

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

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

Published on: May 30, 2014

Quantum Otto engine of a two-level atom with single-mode fields.

Jianhui Wang1, Zhaoqi Wu, Jizhou He

  • 1Department of Physics, Nanchang University, Nanchang 330031, China. physwjh@gmail.com

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 12, 2012
PubMed
Summary
This summary is machine-generated.

We developed a quantum Otto engine using a two-level atom. Maximum efficiency depends on the trap type, offering insights into quantum heat engine optimization.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Last Updated: May 21, 2026

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Area of Science:

  • Quantum thermodynamics
  • Atomic physics
  • Statistical mechanics

Background:

  • Quantum heat engines offer a theoretical framework for exploring thermodynamic principles at the quantum level.
  • Two-level atoms are fundamental systems for studying quantum phenomena and serve as ideal working substances.

Purpose of the Study:

  • To establish and analyze a quantum Otto engine (QOE) model utilizing a two-level atom.
  • To investigate the performance and optimize the efficiency of the QOE under varying conditions.

Main Methods:

  • The study employs a quantum Otto engine model with a two-level atom in a 1D harmonic trap coupled to radiation fields.
  • The semigroup approach is used to derive the time for adiabatic processes.
  • Performance analysis and optimization are conducted for various trap potentials.

Main Results:

  • The quantum Otto engine cycle consists of adiabatic and isochoric processes.
  • The time for adiabatic processes was derived using the semigroup approach.
  • Efficiency at maximum power output is dependent on the trap exponent θ but independent of the energy spectrum index σ.

Conclusions:

  • The developed QOE model provides a platform for studying quantum thermodynamics.
  • Performance optimization is achievable by tuning the trap potential.
  • The findings contribute to understanding the fundamental limits of quantum heat engines.