Category: Index
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Equipartition Theorem
Introduction The equipartition theorem is a fundamental principle of statistical mechanics. It states that for a system in thermal equilibrium, each degree of freedom that appears quadratically in the system’s total energy has an average energy of , where is Boltzmann’s constant and is the absolute temperature. Theoretical Framework for the Equipartition Theorem Degrees of…
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Amplitude Modulation (AM)
Introduction to Amplitude Modulation (AM) Amplitude Modulation (AM) is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. In AM, the strength (amplitude) of the carrier wave is varied in proportion to that of the message signal being sent. Basic Principle of Amplitude Modulation Modulation Process In an…
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Frequency Modulation (FM)
Introduction to Frequency Modulation (FM) Frequency Modulation (FM) is a method of impressing data onto an alternating-current (AC) wave by varying the instantaneous frequency of the wave. This contrasts with amplitude modulation, in which the amplitude of the carrier wave varies, while the frequency remains constant. In analog applications, the instantaneous frequency of the carrier…
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Astigmatism
Introduction Astigmatism is a common vision condition that causes blurred or distorted vision as a result of an irregular curvature of the cornea or the lens of the eye. In an astigmatic eye, the light rays are not converged to a single focus point to provide clear vision. Instead, they are focused on multiple points,…
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Time-Dependent Schrödinger Equation
Introduction The Time-dependent Schrödinger equation (TDSE) is a fundamental equation in quantum mechanics that describes how the quantum state of a physical system changes with time. It is named after Erwin Schrödinger, who formulated the equation in 1926. The Time-dependent Schrödinger Equation The TDSE is given by: Here, is the wavefunction of the system at…
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Turbulence
Introduction Turbulence is a complex phenomenon involving irregular, chaotic fluid flow. Unlike laminar flow, which is smooth and orderly, turbulent flow is characterized by vortices, eddies, and apparent randomness. Physics of Turbulence The onset of turbulence is generally associated with a critical value of the Reynolds number a dimensionless quantity representing the ratio of inertial…
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Electrolysis
Introduction Electrolysis is the process of driving a chemical reaction by applying an external electric current. This process is widely used in various industries for purposes like metal purification, electroplating, and production of certain chemicals. Principles of Electrolysis The principle of electrolysis is based on the movement of ions under the influence of an electric…
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Dirichlet Conditions
Introduction In the context of mathematics and physics, the Dirichlet conditions, named after German mathematician Peter Gustav Lejeune Dirichlet, are a set of conditions that guarantee the existence of the Fourier series for a given function. Definition and the Dirichlet Conditions The Dirichlet conditions can be stated as follows for a function on an interval…
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Dyne (unit)
Introduction The dyne is a unit of force in the centimetre-gram-second (CGS) system of units, which is a part of the metric system. This unit is not widely used in contemporary physics, having been largely superseded by the newton, the SI unit for force. However, the dyne still finds occasional use in certain areas of…
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Erg (unit)
Introduction The erg is a unit of energy and mechanical work in the centimetre-gram-second (CGS) system of units, which is a part of the metric system. While not as widely used today, it is still important in specific fields of physics like astrophysics and physics of plasmas. Defining an Erg One erg is the amount…