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Quantum Numbers02:43

Quantum Numbers

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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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Cyclic Processes And Isolated Systems01:19

Cyclic Processes And Isolated Systems

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A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state. 
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each...
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The Quantum-Mechanical Model of an Atom02:45

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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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Short-distance Transport of Resources02:12

Short-distance Transport of Resources

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Short-distance transport refers to transport that occurs over a distance of just 2-3 cells, crossing the plasma membrane in the process. Small uncharged molecules, such as oxygen, carbon dioxide, and water, can diffuse across the plasma membrane on their own. In contrast, ions and larger molecules require the assistance of transport proteins due to their charge or size. Transport across membranes also occurs within individual cells, playing a variety of essential roles for the plant as a whole.
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Second Order systems II01:18

Second Order systems II

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In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
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First Order Systems01:21

First Order Systems

433
First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
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Related Experiment Video

Updated: Feb 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

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Indistinguishability of Elementary Systems as a Resource for Quantum Information Processing.

Rosario Lo Franco1,2, Giuseppe Compagno2

  • 1Dipartimento di Energia, Ingegneria dell'Informazione e Modelli Matematici, Università di Palermo, Viale delle Scienze, Edificio 9, 90128 Palermo, Italy.

Physical Review Letters
|June 30, 2018
PubMed
Summary

Identical particles can create entanglement when overlapping, a quantum resource previously unconfirmed. This discovery enables new quantum information processing applications like teleportation.

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Area of Science:

  • Quantum Information Science
  • Quantum Physics
  • Quantum Computing

Background:

  • Quantum networks rely on identical systems for quantum information processing.
  • The potential of particle indistinguishability as a quantum resource is an open research question.

Purpose of the Study:

  • To investigate if particle indistinguishability is an exploitable quantum resource.
  • To demonstrate the existence and utility of entanglement from independently prepared identical particles.

Main Methods:

  • Studying independently prepared identical particles.
  • Analyzing spatial overlap of particles.
  • Utilizing separated localized measurements to reveal entanglement.

Main Results:

  • Operational entanglement is demonstrated to exist between independently prepared identical particles when they spatially overlap.
  • This entanglement is proven to be physical and directly exploitable.
  • Entanglement can be manifested through separated localized measurements.

Conclusions:

  • Particle indistinguishability is confirmed as a utilizable quantum resource.
  • The findings pave the way for novel quantum-enhanced applications.
  • This research advances the understanding of fundamental quantum mechanics for practical applications.