Author: Tru Physics
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Problem 8.2 – Griffith’s Intro to QM
Problem 8.2 Find the best bound on for the one-dimensional harmonic oscillator using a trial wave function of the form where is determined by normalization and is an adjustable parameter. Solution: Problem 8.2 Solution (Download)
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Problem 8.1 – Griffith’s Intro to QM
Problem 8.1 Use a gaussian trial function (Equation 8.2) to obtain the lowest upper bound you can on the ground state energy of (a) the linear potential: ; (b) the quartic potential: V(x)=\alpha x^4.$ Solution: Problem 8.1 Solution (Download)
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Chapter 15: Magnetism
15.1 Introduction to Magnetism In this chapter, we will explore the fundamental principles of magnetism, the forces experienced by charged particles in a magnetic field, and the origin of magnetic fields. Understanding magnetism is essential for various applications in physics, such as motors, generators, and transformers. 15.2 Magnetic Fields A magnetic field is a vector…
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Landé g-Factor
Introduction The Landé g-factor, named after Alfred Landé, is a dimensionless quantity that characterizes the magnetic moment and angular momentum of atomic and subatomic particles in quantum physics. This value is a critical part of the Zeeman Effect, where spectral lines split due to an external magnetic field. The g-Factor in Quantum Mechanics In quantum…
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Chapter 14: RC Circuits
14.1 Introduction In this chapter, we will explore RC circuits, which consist of resistors (R) and capacitors (C). These circuits are fundamental in understanding the behavior of capacitors in the presence of resistive elements and the resulting time-dependent voltages and currents. RC circuits play an essential role in various applications, including filtering, integration, differentiation, and…
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Chapter 13: Kirchhoff’s Rules
13.1 Introduction To analyze complex circuits with multiple branches, loops, and nodes, we use Kirchhoff’s rules. These rules, developed by Gustav Kirchhoff, allow us to derive relationships between currents and voltages in a circuit, enabling us to calculate the unknown values. In this chapter, we will discuss Kirchhoff’s rules and how to apply them to…
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Mesons
Introduction Mesons are a category of subatomic particles composed of a quark and an antiquark pair, bound together by the strong nuclear force. They are classified as bosons due to their integral spin. Basic Properties of Mesons Mesons are defined by the composition of a quark-antiquark pair. The quark content determines the properties of the…
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Magnetoresistance
Introduction Magnetoresistance is the property of a material to change its electrical resistance in response to an applied magnetic field. This quantum mechanical phenomenon has profound applications in modern electronics and computing. Basic Explanation When a magnetic field is applied to a conductive material, the trajectories of the charge carriers (electrons or holes) can be…
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Quantum Tunneling
Introduction Quantum tunneling is a quantum mechanical phenomenon where particles can penetrate through a potential energy barrier that they could not surmount according to classical physics. It arises from the wave-like nature of particles described by the principles of quantum mechanics. Basic Explanation of Quantum Tunneling In classical physics, a particle would need to have…
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Mach’s Principle
Introduction Mach’s Principle, named after the physicist Ernst Mach, is a postulate that discusses the relationship between the distribution of matter in the universe and the local behavior of an inertial frame. Mach’s Principle has had a significant influence on the development of general relativity and cosmology, even though it is not precisely defined. Basic…