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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 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.

The Uncertainty Principle

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...

Space-Time Curvature and the General Theory of Relativity

Space-Time Curvature and the General Theory of Relativity

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...

The Buckingham Pi Theorem

The Buckingham Pi Theorem

The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.

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...

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Related Experiment Video

Updated: Mar 30, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Quantum Hilbert Hotel.

Václav Potoček^1,2, Filippo M Miatto^3,4, Mohammad Mirhosseini⁵

¹SUPA School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom.

Physical Review Letters

|November 10, 2015

Summary

This summary is machine-generated.

Researchers demonstrate a quantum mechanics analog of Hilbert's hotel paradox. This protocol maps infinite quantum states, creating unoccupied levels for applications in quantum information science.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs

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Area of Science:

Quantum Mechanics
Mathematical Physics

Background:

David Hilbert's paradox of the infinite hotel illustrates concepts of infinity.
Continuous-variable quantum mechanics utilizes infinite-dimensional state spaces.

Purpose of the Study:

To demonstrate an analog of Hilbert's hotel paradox within quantum mechanics.
To develop a protocol for manipulating infinite eigenbasis amplitudes.

Main Methods:

Devised a protocol to map amplitudes of an infinite eigenbasis.
Mapped amplitudes to twice their original quantum number coherently and deterministically.
Experimentally realized the protocol on the orbital angular momentum of a paraxial field.

Main Results:

Successfully created an analog of Hilbert's hotel paradox in a quantum system.
Generated infinitely many unoccupied levels by doubling quantum numbers.
Demonstrated a novel non-Gaussian operation.

Conclusions:

The developed protocol offers a new method for manipulating quantum states.
Potential applications include enhancing NOON states sensitivity, increasing channel capacity, and channel multiplexing.