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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 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...
Real Number Operations01:27

Real Number Operations

The concept of real numbers includes all the values that can be represented on a continuous number line. The system began with basic counting values used for enumeration. It later expanded to include values that represent the absence of quantity and opposites of the counting values. When situations required expressing parts of a whole or dividing quantities evenly, values capable of representing such proportions were developed. When written using decimal notation, these values can end or repeat...
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...
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.
Electronic Structure of Atoms02:28

Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers:  n, l, ml, and...

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Related Experiment Video

Updated: Jul 8, 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

Quantum Mechanics Based on Real Numbers: A Consistent Description.

Pedro Barrios Hita1,2, Anton Trushechkin2, Hermann Kampermann2

  • 1German Aerospace Center (DLR), Institute of Software Technology, Sankt Augustin, Germany.

Physical Review Letters
|July 7, 2026
PubMed
Summary
This summary is machine-generated.

Complex numbers in quantum mechanics are not essential. A new study shows real-number quantum mechanics can explain all multipartite experiments, suggesting complex numbers are a matter of convenience, not necessity.

Related Experiment Videos

Last Updated: Jul 8, 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
  • Foundations of Quantum Mechanics

Background:

  • Complex numbers are fundamental to standard quantum mechanics.
  • The necessity of complex numbers in quantum theory is an ongoing debate.
  • Previous research suggested real-number quantum theories could be falsified.

Purpose of the Study:

  • To investigate if real-number quantum mechanics can reproduce all predictions of complex-number quantum mechanics for multipartite systems.
  • To determine if real-valued quantum mechanics is falsifiable.

Main Methods:

  • Developed a real-number quantum mechanics model based on a physically motivated postulate for composite systems.
  • Compared the predictive power of the real-valued model with the standard complex-valued quantum mechanics for multipartite experiments.

Main Results:

  • A real-number quantum mechanics was constructed that accurately reproduces predictions for all multipartite quantum experiments.
  • The developed real-valued quantum mechanics cannot be falsified by these experiments.

Conclusions:

  • The use of complex numbers in quantum mechanics is a matter of convenience, not fundamental necessity.
  • Real-number quantum mechanics is a viable alternative for describing multipartite quantum phenomena.
  • Multipartite experiments do not falsify real-valued quantum mechanics.