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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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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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Application of the Linear Momentum Equation01:15

Application of the Linear Momentum Equation

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The application of the linear momentum equation can be used to analyze the forces needed to hold a 180-degree pipe bend in place with flowing water. In this case, water flows through the bend with a constant cross-sectional area of 0.01 square meters and a flow velocity of 15 meters per second. The pressure at the entrance is 0.2 Megapascals and the pressure at the exit is 0.16 Megapascals.
The goal is to determine the force components in the x and y directions to hold the pipe in place. Since...
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Linear time-invariant Systems01:23

Linear time-invariant Systems

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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
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2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

1.4K
Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
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The Nernst Equation02:59

The Nernst Equation

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Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.
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Related Experiment Video

Updated: Jan 28, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor
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Gradient Echo Quantum Memory in Warm Atomic Vapor

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Quantum Algorithms for Systems of Linear Equations Inspired by Adiabatic Quantum Computing.

Yiğit Subaşı1, Rolando D Somma1, Davide Orsucci2

  • 1Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review Letters
|March 2, 2019
PubMed
Summary
This summary is machine-generated.

We developed two quantum algorithms using evolution randomization to solve linear equations. These algorithms offer significant speed-ups and are simpler to implement than previous methods.

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Area of Science:

  • Quantum Computing
  • Quantum Algorithms
  • Linear Algebra

Background:

  • Solving systems of linear equations (Ax=b) is a fundamental problem in science and engineering.
  • Adiabatic quantum computing offers a potential pathway for quantum speed-ups.
  • Existing quantum algorithms for linear systems often require complex implementations or large resources.

Purpose of the Study:

  • To present novel quantum algorithms for preparing solutions to linear systems.
  • To achieve efficient time complexities based on condition number and precision.
  • To explore simpler, Hamiltonian-based approaches to quantum linear system solving.

Main Methods:

  • Utilizing evolution randomization, a variant of adiabatic quantum computing.
  • Constructing algorithms with Hamiltonians as linear combinations of A, projector onto |b⟩, and Pauli operators.
  • Implementing algorithms via Hamiltonian simulation for gate-based quantum computers.

Main Results:

  • Two algorithms with time complexities O(κ²log(κ)/ε) and O(κlog(κ)/ε) were developed.
  • The algorithms are conceptually simple, easy to implement, and do not require ancillary systems.
  • The second algorithm demonstrates near-optimality concerning the condition number κ.

Conclusions:

  • The proposed quantum algorithms provide an efficient and accessible method for solving linear systems.
  • These findings highlight the utility of Hamiltonian-based quantum computing models.
  • The research offers an exponential quantum speed-up under specific assumptions, advancing the field of quantum computation.