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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...
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...
The de Broglie Wavelength02:32

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 Uncertainty Principle04:08

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 mathematically...
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...
Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...

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Related Experiment Video

Updated: May 13, 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

Schrödinger equation revisited.

Wolfgang P Schleich1, Daniel M Greenberger, Donald H Kobe

  • 1Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQ(ST)), Universität Ulm, D-89069 Ulm, Germany.

Proceedings of the National Academy of Sciences of the United States of America
|March 20, 2013
PubMed
Summary
This summary is machine-generated.

Researchers derived the time-dependent Schrödinger equation from classical statistical mechanics. This reveals quantum mechanics

Related Experiment Videos

Last Updated: May 13, 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 Physics
  • Statistical Mechanics
  • Mathematical Physics

Background:

  • The time-dependent Schrödinger equation is fundamental to quantum physics.
  • Its origins and the underlying mathematical principles are not widely understood.

Purpose of the Study:

  • To derive the time-dependent Schrödinger equation from a novel perspective.
  • To elucidate the connection between classical statistical mechanics and quantum mechanics.
  • To clarify the origins of quantum mechanics' linearity.

Main Methods:

  • Generalization of the Hamilton-Jacobi formulation of classical statistical mechanics.
  • Derivation from a mathematical identity.

Main Results:

  • The Schrödinger equation can be obtained through a generalized classical statistical mechanics framework.
  • Demonstrated the intimate link between quantum mechanics' linearity and the coupling of wave amplitude and phase.

Conclusions:

  • The study provides a new perspective on the origin of the Schrödinger equation.
  • Highlights the deep connection between classical and quantum physics formulations.