Category: Index
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Problem 1.17 – Griffith’s Intro to QM
Problem 1.17 Suppose you wanted to describe an unstable particle, that spontaneously disintegrates with a “lifetime” In that case the total probability of finding the particle somewhere should not be constant, but should decrease at (say) an exponential rate: A crude way of achieving this result is as follows. In Equation 1.24 we tacitly assumed…
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Kramers-Kronig Relations
Introduction The Kramers-Kronig relations are fundamental theorems in the fields of physics and engineering, specifically in optics and electrical engineering. These relations connect the real and imaginary parts of any complex function that obeys certain causality conditions. They are primarily used in the analysis of linear, passive systems. Mathematical Formulation of the Kramers-Kronig Relations Let…
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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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Torricelli’s Law
Introduction Torricelli’s Law describes the speed of fluid flowing under the force of gravity from a container through a small opening or orifice. It’s a fundamental principle in fluid dynamics named after the Italian scientist Evangelista Torricelli. Statement of Torricelli’s Law Torricelli’s Law states that the speed of the efflux (outflow) of a fluid under…
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Electron Volt (eV)
Introduction The electron volt (eV) is a unit of energy particularly convenient in the realm of atomic, nuclear, and particle physics. It’s associated with the energy gained or lost by an electron moving across an electric potential difference of one volt. Defining the Electron Volt An electron volt is defined as the amount of kinetic…
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Poynting Vector
Introduction The Poynting vector is a fundamental concept in electromagnetism representing the directional energy flux density (the rate of energy transfer per unit area, in Watts per square meter) of an electromagnetic field. It is named after its inventor, the physicist John Henry Poynting. Definition the Poynting Vector The Poynting vector is defined as the…
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Wurtzite
Introduction The Wurtzite structure, named after the mineral Wurtzite, is a crystal structure common to many binary compounds. It represents a hexagonal close-packed array (hcp) and is a variant of the zinc blende structure. The structure is common to many semiconductors such as GaN, ZnS, and ZnO. Basic Description of Wurtzite The Wurtzite structure can…
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Twin Paradox
Introduction The Twin Paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the other twin, who has stayed on Earth, has aged more. This seemingly paradoxical outcome arises from the relativistic effects of time dilation.…
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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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Mie Scattering
Introduction Mie scattering is a solution of Maxwell’s equations for the scattering of an electromagnetic plane wave by a homogeneous sphere. The term “Mie scattering” suggests scattering by particles that are similar in size to, or larger than, the wavelength of light. It is named after Gustav Mie, who first solved the scattering problem for…