Related Experiment Video
Updated: Aug 9, 2025
08:04
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
Published on: May 27, 2020
8.5K
Pauli's Electron in Ehrenfest and Bohm Theories, a Comparative Study
1Department of Electrical & Electronic Engineering, Faculty of Engineering, Ariel University, Ariel 40700, Israel.
Entropy (Basel, Switzerland)
|February 25, 2023
Summary
This study compares two interpretations of electron behavior at low speeds. It contrasts the Copenhagen interpretation
Area of Science:
- Quantum Mechanics
- Electron Dynamics
Background:
- Electrons at low speeds are described by Pauli's equation, a low-velocity limit of the Dirac equation.
- Two interpretations exist: the Copenhagen interpretation and Bohm's approach.
Purpose of the Study:
- To compare the electron trajectory from Bohm's interpretation with the electron expectation value trajectory from the Copenhagen interpretation using the Ehrenfest theorem.
- To analyze similarities and differences between these two quantum mechanical approaches.
Main Methods:
- Solving Pauli's equation for the electron wave function.
- Calculating the electron expectation value trajectory via the Ehrenfest theorem.
- Deriving the electron velocity field from the Pauli wave function for Bohm's approach.
Main Results:
- The study analyzes both similarities and differences in electron trajectories predicted by Bohm's interpretation and the Ehrenfest theorem.
- Detailed comparison of the two distinct quantum mechanical viewpoints.
Conclusions:
- The comparison offers insights into the foundational interpretations of quantum mechanics for non-relativistic electrons.
- Highlights the divergence and convergence of deterministic and probabilistic electron trajectory concepts.
Related Concept Videos
03:06The Pauli Exclusion Principle
42.6K
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
42.6K
02:18The Bohr Model
59.1K
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...
59.1K
02:45The Quantum-Mechanical Model of an Atom
42.7K
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.
42.7K
04:08The Uncertainty Principle
23.5K
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...
23.5K
01:18Electron Orbital Model
68.2K
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 first shell is closest to the nucleus, and it has only one subshell with a single spherical orbital called the...
68.2K
02:32The de Broglie Wavelength
26.0K
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...
26.0K