Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

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.

Molecular Orbital Theory I

Molecular Orbital Theory I

Overview of Molecular Orbital Theory

Molecular Orbital Theory II

Molecular Orbital Theory II

Molecular Orbital Energy Diagrams

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 Bohr Model

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...

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...

You might also read

Related Articles

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

Sort by

Same author

The effect of an optical cavity on diabatic tunneling in an ensemble of symmetric double-well systems.

The Journal of chemical physics·2025

Same author

Semiclassical second order vibrational perturbation theory for hopping rates of H and D atoms on Pt(111) and H on Ru(0001).

Physical chemistry chemical physics : PCCP·2025

Same author

Theory of Nonadiabatic Tunneling Splitting.

The journal of physical chemistry letters·2025

Same author

Modified vibrational perturbation theory as applied to the collinear H + H2 and D + H2 reactions.

The Journal of chemical physics·2025

Same author

Grazing incidence fast atom diffraction: general considerations, semiclassical perturbation theory and experimental implications.

Physical chemistry chemical physics : PCCP·2024

Same author

Is Quantum Above-Barrier Reflection Important for Molecular Barrier Crossing Rates?

Journal of chemical theory and computation·2024

Same journal

Accurate Density Functional Theory Forces for Charged Noncovalent Complexes.

The journal of physical chemistry letters·2026

Same journal

Dopant-Centered versus Intersite Synergistic Mechanisms in H<sub>2</sub> Dissociation on Single-Atom Alloys.

The journal of physical chemistry letters·2026

Same journal

Post-Translational Modification as an Allosteric Switch in Hsp90: How Dual Phosphorylation Locks Chaperone Complexes into Hyperstabilized States.

The journal of physical chemistry letters·2026

Same journal

LHCSR1 Functions as a Dimmer Switch for Light Harvesting.

The journal of physical chemistry letters·2026

Same journal

Sparse Linear Surrogates Match Neural Network Potentials on the SPICE Biomolecular Benchmark with Three Orders of Magnitude Smaller Training Sets.

The journal of physical chemistry letters·2026

Same journal

Solid-State NMR Quantification of Brønsted-Lewis Acid Site Cooperativity in Zeolites for Glucose Conversion.

The journal of physical chemistry letters·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jan 17, 2026

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

Improved Semiclassical Quantization of Bound States.

¹Chemical and Biological Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel.

The Journal of Physical Chemistry Letters

|January 14, 2026

Summary

This summary is machine-generated.

A modified semiclassical quantization formula accurately estimates zero-point energy by incorporating an energy shift derived from perturbation theory. This improved formula enhances energy eigenvalue predictions for various potentials.

More Related Videos

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Related Experiment Videos

Last Updated: Jan 17, 2026

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

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Area of Science:

Quantum mechanics
Theoretical chemistry
Spectroscopy

Background:

The Brillouin, Wentzel, and Kramers (BWK) semiclassical quantization formula, a foundational tool for vibrational analysis, has limitations in accurately predicting zero-point energy.
Existing methods often require complex calculations or yield approximate results for specific potentials.

Purpose of the Study:

To address the deficiency in the standard BWK formula regarding zero-point energy estimation.
To develop a modified semiclassical quantization approach that provides more accurate energy eigenvalues.

Main Methods:

Introduction of a simple energy shift into the action expression within the BWK formula.
Magnitude of the energy shift determined by second-order vibrational perturbation theory.
Expansion and comparison of the modified formula with existing theoretical frameworks.

Main Results:

The modified semiclassical quantization formula is shown to be equivalent to second-order vibrational perturbation theory upon expansion.
Demonstrated improvement in energy eigenvalue predictions for the symmetric Rosen-Morse potential.
Achieved accurate resonance energy estimates for a cubic potential, outperforming standard BWK and second-order perturbation theory.

Conclusions:

The developed modified semiclassical quantization method offers a more accurate approach to calculating vibrational energy levels.
This enhanced formula provides a valuable tool for theoretical chemistry and spectroscopy, particularly for systems with complex potentials.