Author: Tru Physics
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Problem 1.13 – Griffith’s Intro to QM
Problem 1.13 Check your results in Problem 1.11(b) with the following “numerical experiment.” The position of the oscillator at time t is You might as well take (that sets the scale for time) and (that sets the scale for length). Make a plot of at 10,000 random times, and compare it with Hint: In Mathematica,…
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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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Chapter 21: Superconductivity
21.1 Introduction In this chapter, we will discuss superconductivity, a remarkable phenomenon in which certain materials exhibit zero electrical resistance when cooled below a critical temperature. Superconductivity has important applications in various fields, including medical imaging, transportation, and energy transmission. 21.2 Superconductivity Basics Superconductivity is a state in which a material exhibits zero electrical resistance,…
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Chapter 20: Faraday’s Law, Lenz’s Law
20.1 Introduction In this chapter, we will explore Faraday’s law of electromagnetic induction and Lenz’s law. Faraday’s law states that a change in the magnetic field within a closed loop induces an electromotive force (EMF) in the loop. Lenz’s law describes the direction of the induced EMF and helps us understand the principle of energy…
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Chapter 19: Ampere’s Law
19.1 Introduction In this chapter, we will introduce Ampere’s law, which relates the magnetic field around a closed loop to the total electric current passing through the loop. Ampere’s law is an essential tool for calculating the magnetic fields generated by steady currents in wires and other conductive materials. 19.2 Ampere’s Law Ampere’s law states…
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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…