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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. Schrödinger...

Classical Mechanics

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Classical mechanics provides a mathematical description of the motion of bodies under the influence of forces. A key principle within this field is the work-energy theorem, which establishes a bridge between the net work done on an object and its kinetic energy.The work-energy theorem states that the net work done on a particle by all the forces acting on it equals the change in its kinetic energy.In simple terms, the work-energy theorem is a method to analyze the effects of forces on an...

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Related Experiment Video

Updated: Jun 29, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Quantum simulations of classical annealing processes.

R D Somma¹, S Boixo, H Barnum

¹Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5, Canada. rsomma@perimeterinstitute.ca

Physical Review Letters

|October 15, 2008

Summary

This study introduces a quantum algorithm for combinatorial optimization, simulating classical annealing. It achieves a quadratic speedup using quantum walks and the quantum Zeno effect, improving efficiency for complex problem-solving.

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Last Updated: Jun 29, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

Quantum Computing
Computational Optimization
Algorithm Development

Background:

Combinatorial optimization problems are computationally intensive.
Classical simulated annealing is a common heuristic approach.
Existing methods face scalability challenges for large problem instances.

Purpose of the Study:

To develop a novel quantum algorithm for solving combinatorial optimization problems.
To leverage quantum phenomena for enhanced computational efficiency.
To provide a quadratic improvement over classical simulated annealing.

Main Methods:

Quantum simulation of classical simulated annealing.
Utilizing quantum walks for state exploration.
Employing the quantum Zeno effect via evolution randomization.

Main Results:

The quantum algorithm achieves a quadratic speedup.
It requires O(1/sqrt delta) steps, compared to O(1/delta) for classical methods.
Bounded error probability in finding optimal solutions is guaranteed.

Conclusions:

The proposed quantum algorithm offers a significant advancement in solving combinatorial optimization.
Quantum simulation of annealing provides a powerful framework for complex problems.
This approach demonstrates the potential of quantum computing for practical applications.