Author: Tru Physics
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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…
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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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Problem 9.3 – Griffith’s Intro to QM
Problem 9.3 Use Equation 9.23 to calculate the approximate transmission probability for a particle of energy that encounters a finite square barrier of height and width Compare your answer with the exact result (Problem 2.33), to which it should reduce in the WKB regime Solution: Problem 9.3 Solution (Download)
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Problem 9.2 – Griffith’s Intro to QM
Problem 9.2 An alternative derivation of the WKB formula (Equation 9.10) is based on an expansion in powers of . Motivated by the free-particle wave function, we write where is some complex function. (Note that there is no loss of generality here—any nonzero function can be written in this way.) (a) Put this into Schrödinger’s…
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Chapter 18: The Magnetic Field of a Moving Charge
18.1 Introduction In this chapter, we will discuss the magnetic field produced by moving charges, such as electrons and ions, and how it affects the motion of other charged particles. Understanding the magnetic field of a moving charge is essential for various applications, including the design of particle accelerators and the analysis of plasma behavior…
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Chapter 17: The Direct-Current (DC) Motor
17.1 Introduction In this chapter, we will discuss the principles behind the operation of direct-current (DC) motors. These motors convert electrical energy into mechanical energy by generating torque through the interaction of electric currents and magnetic fields. 17.2 Structure of a DC Motor A DC motor consists of two main components: the stator and the…
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Chapter 16: Motion in Magnetic Fields
16.1 Introduction In this chapter, we will explore the motion of charged particles in magnetic fields. Understanding the behavior of particles in magnetic fields is important for various applications, including particle accelerators, magnetic confinement fusion, and magnetic resonance imaging. 16.2 Motion of Charged Particles in a Uniform Magnetic Field When a charged particle enters a…