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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...
Fermi Level Dynamics01:12

Fermi Level Dynamics

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Quantum Numbers02:43

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 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.
Electron Orbital Model01:18

Electron Orbital Model

Orbitals are the areas outside of the atomic nucleus where electrons are most likely to reside. They are characterized by different energy levels, shapes, and three-dimensional orientations. The location of electrons is described most generally by a shell or principal energy level, then by a subshell within each shell, and finally, by individual orbitals found within the subshells.The first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...

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Updated: Jun 10, 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

A semiclassical correction for quantum mechanical energy levels.

Alexey L Kaledin1, C William McCurdy, William H Miller

  • 1Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA.

The Journal of Chemical Physics
|August 17, 2010
PubMed
Summary

This study introduces a semiclassical method to correct molecular energy levels from quantum calculations. The approach refines energy eigenvalues by addressing errors in semiclassical approximations of energy corrections.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Spectroscopy

Background:

  • Variational calculations provide approximate molecular energy levels as eigenvalues.
  • Trial wave functions in variational methods introduce errors (DeltaE) in energy level calculations.
  • Accurate energy levels are crucial for understanding molecular behavior and predicting spectra.

Purpose of the Study:

  • To develop a semiclassical method for correcting molecular energy levels obtained from quantum mechanical variational calculations.
  • To identify the source of errors in variational energy level calculations.
  • To improve the accuracy of computed molecular energies.

Main Methods:

  • A semiclassical approach is proposed to correct energy levels from variational calculations.
  • The method involves expressing the energy correction (DeltaE) using Green's function.
  • Semiclassical approximations are applied to the Green's function, utilizing the time evolution operator.

Main Results:

  • The proposed semiclassical method effectively corrects molecular energy levels.
  • Calculations on test problems (quartic potential, H2O, H2CO) validate the method.
  • The primary source of error in total energy is attributed to the semiclassical approximation of DeltaE.

Conclusions:

  • The developed semiclassical method offers a viable way to enhance the accuracy of variational energy calculations.
  • This approach provides a more precise determination of molecular energy levels.
  • The findings have implications for computational chemistry and molecular spectroscopy.