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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...
2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

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...
2D NMR: Overview of Heteronuclear Correlation Techniques01:18

2D NMR: Overview of Heteronuclear Correlation Techniques

Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other axis.
Calculation of First-Law Quantities II01:24

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The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...
Calculation of First Law Quantities I01:25

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Quantum Numbers02:43

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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.

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Related Experiment Video

Updated: Jun 27, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Correlation functions in quantized Hamilton dynamics and quantal cumulant dynamics.

Yuriy V Pereverzev1, Andrey Pereverzev, Yasuteru Shigeta

  • 1Department of Chemistry, University of Washington, Seattle, Washington 98195-1700, USA.

The Journal of Chemical Physics
|December 3, 2008
PubMed
Summary
This summary is machine-generated.

Quantized Hamilton dynamics (QHD) and quantal cumulant dynamics (QCD) offer efficient semiclassical approximations for two-time correlation functions. The second-order QHD/QCD method accurately reproduces quantum mechanical results with minimal computational cost.

Related Experiment Videos

Last Updated: Jun 27, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Quantum dynamics
  • Computational chemistry
  • Statistical mechanics

Background:

  • Two-time correlation functions (CFs) are crucial for describing quantum systems.
  • Accurate calculation of CFs often requires computationally intensive quantum mechanical methods.
  • Existing semiclassical methods face challenges in accurately capturing the dynamics of CFs.

Purpose of the Study:

  • To develop and validate an efficient semiclassical approach for calculating two-time correlation functions.
  • To assess the accuracy of Quantized Hamilton Dynamics (QHD) and Quantal Cumulant Dynamics (QCD) for CFs.
  • To demonstrate the capability of the second-order QHD/QCD approximation in reproducing quantum mechanical results.

Main Methods:

  • Application of Quantized Hamilton Dynamics (QHD) and Quantal Cumulant Dynamics (QCD).
  • Utilizing a closure approximation to truncate the infinite hierarchy of correlation functions.
  • Testing the method on a simple nonlinear system to evaluate its performance.

Main Results:

  • The developed semiclassical approach provides an efficient approximation to quantum mechanics.
  • For a nonlinear system, the real part of the classical CF exhibited perfect oscillation, and the imaginary part was zero.
  • The second-order QHD/QCD approximation successfully reproduced both real and imaginary parts of the quantum-mechanical CF.

Conclusions:

  • The second-order QHD/QCD approximation offers a computationally inexpensive yet accurate method for calculating two-time correlation functions.
  • This approach bridges the gap between classical and quantum descriptions of dynamics.
  • QHD and QCD are promising tools for studying complex quantum systems where full quantum mechanical treatment is intractable.