Tag: Quantum
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Ward–Takahashi Identity
Introduction The Ward–Takahashi Identity, named after physicists J.C. Ward and Y. Takahashi, is a key result in quantum electrodynamics (QED) and quantum field theory (QFT). It ensures the conservation of electric charge in QED, and more generally, the conservation of current in QFT. Statement of the Ward–Takahashi Identity Identity The Ward-Takahashi identity can be written…
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Photon Polarization
Introduction Photon polarization refers to the quantum mechanical description of the classical phenomenon of electromagnetic polarization. In quantum mechanics, the polarization state of a photon is modeled with a quantum bit, or qubit, which is a basic unit of quantum information. Basics of Photon Polarization In classical electrodynamics, the polarization of an electromagnetic wave describes…
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Ehrenfest’s Theorem
Introduction Ehrenfest’s theorem is a fundamental principle in quantum mechanics that reveals a deep connection between quantum mechanics and classical mechanics. It essentially bridges the gap between the quantum and classical descriptions of physical systems. Basics of Ehrenfest’s Theorem Ehrenfest’s theorem states that the average value of an observable (such as position or momentum) in…
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Density Functional Theory (DFT)
Introduction Density Functional Theory (DFT) is a computational quantum mechanical modelling method used to investigate the electronic structure of many-body systems, especially atoms, molecules, and the condensed phases. The Basics of DFT The fundamental premise behind DFT is the Hohenberg-Kohn theorem, which states that the ground state properties of a many-electron system are uniquely determined…
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Aharonov–Bohm Effect
Introduction The Aharonov–Bohm effect is a quantum mechanical phenomenon that demonstrates how a charged particle is affected by electromagnetic fields, despite being in regions of apparently zero electromagnetic fields. This effect illustrates the fundamental role of potentials in quantum mechanics, in contrast to classical physics where fields play the dominant role. Aharonov–Bohm Electromagnetic Potential The…
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Landé g-Factor
Introduction The Landé g-factor, named after Alfred Landé, is a dimensionless quantity that characterizes the magnetic moment and angular momentum of atomic and subatomic particles in quantum physics. This value is a critical part of the Zeeman Effect, where spectral lines split due to an external magnetic field. The g-Factor in Quantum Mechanics In quantum…
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Quantum Tunneling
Introduction Quantum tunneling is a quantum mechanical phenomenon where particles can penetrate through a potential energy barrier that they could not surmount according to classical physics. It arises from the wave-like nature of particles described by the principles of quantum mechanics. Basic Explanation of Quantum Tunneling In classical physics, a particle would need to have…
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Stark Effect
Overview The Stark Effect, named after German physicist Johannes Stark, is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external electric field. The amount of shifting or splitting is proportional to the strength of the electric field. This is an important phenomenon in both atomic physics…
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Unruh Effect
Introduction The Unruh effect is a theoretical prediction in quantum field theory and is one of the results showing the deep connections between quantum physics, thermodynamics, and relativity. Proposed by William G. Unruh in 1976, it suggests that an accelerating observer will be in a thermal state – in other words, they will observe a…
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Hartman Effect
Introduction The Hartman Effect is a quantum mechanical phenomenon in which the tunneling time for a particle to pass through a potential barrier becomes independent of the barrier’s width when the width is sufficiently large. Named after Thomas Hartman, who first described it in 1962, this effect appears to violate the principle of causality because…