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The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

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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.
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Cooperative Allosteric Transitions01:58

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Quantum Numbers02:43

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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.
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Norton's Theorem01:14

Norton's Theorem

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Norton's theorem is a fundamental principle stating that a linear two-terminal circuit can be substituted with an equivalent circuit, which comprises a current source (ⅠN) in parallel with a resistor (RN). Here, ⅠN represents the short-circuit current flowing through the terminals, and RN stands for the input or equivalent resistance at the terminals when all independent sources are deactivated. This implies that the circuit illustrated in Figure (a) can be exchanged with the...
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Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
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Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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Related Experiment Video

Updated: Sep 23, 2025

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

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Transitioning organizations to post-quantum cryptography.

David Joseph1, Rafael Misoczki2, Marc Manzano3

  • 1SandboxAQ, Palo Alto, CA, USA. david.joseph@sandboxaq.com.

Nature
|May 13, 2022
PubMed
Summary

Quantum computing threatens current encryption. Organizations must transition to quantum-resistant cryptography (PQC) algorithms, a complex process requiring careful planning for security and performance.

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Area of Science:

  • Cryptography and Quantum Computing Security

Background:

  • Quantum computers, leveraging Shor's algorithm, pose a significant threat to current public key cryptography.
  • The development of quantum-resistant cryptography (PQC) algorithms is crucial for future data security.

Purpose of the Study:

  • To provide an organizational perspective on the transition to post-quantum cryptography (PQC).
  • To outline strategies for mitigating risks during the PQC migration process.

Main Methods:

  • Discussion of PQC transition timelines and leading protection strategies.
  • Analysis of hybrid approaches combining pre-quantum and PQC algorithms.
  • Recommendations for organizational PQC adoption.

Main Results:

  • The PQC transition is a multi-decade process with complex security, performance, and implementation challenges.
  • Hybrid cryptography approaches can minimize risks during the migration.
  • Early experimentation with suggested PQC standards is advised.

Conclusions:

  • A proactive and strategic approach is essential for a smooth and timely PQC transition.
  • Organizations need to consider security, performance, and implementation ease for successful PQC adoption.