Tag: Quantum
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d’Alembert Operator
Introduction The d’Alembert operator, also known as the d’Alembertian or wave operator, is a second-order differential operator that is essential in the study of wave equations in classical field theory, electromagnetism, and quantum mechanics. The d’Alembert Operator Definition The d’Alembert operator is defined in the Minkowski spacetime, the setting for the special theory of relativity.…
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Pauli Exclusion Principle
Introduction The Pauli Exclusion Principle is a fundamental concept in quantum mechanics, formulated by Austrian physicist Wolfgang Pauli in 1925. This principle is crucial for understanding the behavior of electrons in atoms and forms the basis for the structure of the periodic table of elements. Statement of the Pauli Exclusion Principle The Pauli Exclusion Principle…
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Optics
Introduction Optics is a branch of physics that studies the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Nature of Light Light is an electromagnetic wave, and its speed in a vacuum…
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Quantum Electrodynamics (QED)
Introduction Quantum Electrodynamics (QED) is a quantum field theory that describes how light and matter interact. It is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical…
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Quantum Entanglement
Introduction Quantum entanglement is a quantum mechanical phenomenon in which two or more particles become linked and instantaneously affect each other’s state no matter how far apart they are. This entanglement is a fundamental aspect of quantum mechanics, with broad implications in areas such as quantum computing, quantum cryptography, and quantum teleportation. Basics of Quantum…
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Quantum Field Theory (QFT)
Introduction Quantum Field Theory (QFT) is a theoretical framework that combines the principles of quantum mechanics and special relativity to describe the behavior of quantum particles and fields. It is the basis for our understanding of elementary particle physics, and it underpins the standard model of particle physics. Basics of Quantum Fields In QFT, particles…
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Quantum Mechanics
Introduction Quantum Mechanics is the branch of physics that describes the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. It is one of the fundamental theories of physics, alongside General Relativity, and has been remarkably successful in predicting experimental results. Wave-Particle Duality One of the cornerstone concepts in…
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Nanotechnology
Introduction Nanotechnology is the manipulation of matter on an atomic, molecular, and supramolecular scale. Generally, nanotechnology deals with structures sized between 1 to 100 nanometers in at least one dimension, and involves developing materials or devices within that size. Quantum Size Effect When particle sizes approach the nanoscale, quantum effects can begin to dominate the…
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Magnetic Monopoles
Introduction Magnetic monopoles are hypothetical particles that carry a single, isolated magnetic pole – either a north pole or a south pole. In contrast, every known particle that carries a magnetic field has both a north and a south pole. The concept of magnetic monopoles arises from the symmetry in Maxwell’s equations and the concept…
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Klein-Gordon Equation
Introduction The Klein-Gordon equation is a relativistic wave equation, related to the Schrödinger equation, and is a cornerstone of quantum field theory. It was developed by Oskar Klein and Walter Gordon in 1926. The Klein-Gordon Equation The Klein-Gordon equation describes scalar particles, such as mesons (quarks and antiquarks bound together) in quantum field theory. In…