Tru Physics

Author: Tru Physics

  • Cauchy-Riemann Equations

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    Introduction The Cauchy-Riemann equations are a pair of partial differential equations which provide necessary and sufficient conditions for a complex function to be holomorphic. A holomorphic function is complex differentiable, i.e., it is a function that is differentiable when regarded as a function on the real plane . Complex Functions and Differentiability A complex function…

  • Dot Product

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    Introduction The dot product, also known as the scalar product, is a fundamental operation in the field of vector algebra. It operates on two vectors to produce a scalar, or single number. Definition of the Dot Product For two vectors and , the dot product is defined as: This operation multiplies corresponding components of and…

  • Cross Product

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    Introduction The cross product (also known as the vector product) is an operation on two vectors in three-dimensional space. It results in a vector that is orthogonal (perpendicular) to both of the original vectors, with a magnitude equal to the area of the parallelogram that the vectors span. Basics of the Cross Product Given two…

  • Chapter 23: RL and LC Circuits

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    23.1 Introduction In this chapter, we will explore RL (resistor-inductor) and LC (inductor-capacitor) circuits. These circuits are essential to understanding the transient behavior and oscillations that occur in various electrical and electronic applications. 23.2 RL Circuits An RL circuit consists of a resistor and an inductor connected in series. When a voltage is applied across…

  • Chapter 24: The LRC Series Circuit

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    24.1 Introduction In this chapter, we will explore LRC series circuits, which combine resistors inductors and capacitors in series. These circuits are critical in various applications, including filters, oscillators, and transient suppression. 24.2 The LRC Series Circuit An LRC series circuit consists of a resistor an inductor and a capacitor connected in series. The response…

  • Chapter 22: Mutual Inductance

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    22.1 Introduction In this chapter, we will explore the concept of mutual inductance, which describes how the magnetic field generated by one coil affects another nearby coil. Mutual inductance plays an essential role in understanding transformers, which are used to convert alternating current (AC) voltages and currents in various applications, such as power transmission. 22.2…

  • Problem 2.22 – Griffith’s Intro to QM

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    Problem 2.22 Evaluate the following integrals: (a) (b) (c) Solution: Problem 2.22 Solution (Download)

  • Problem 2.18 – Griffith’s Intro to QM

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    Problem 2.18 Find the probability current, (Problem 1.14) for the free particle wave function Equation 2.95. Which direction does the probability flow? Solution: Problem 2.18 Solution (Download)

  • Problem 2.17 – Griffith’s Intro to QM

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    Problem 2.17 Show that and are equivalent ways of writing the same function of and determine the constants and in terms of and and vice versa. Comment: In quantum mechanics, when the exponentials represent traveling waves, and are most convenient in discussing the free particle, whereas sines and cosines correspond to standing waves, which arise…

  • Problem 2.15 – Griffith’s Intro to QM

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    Problem 2.15 Use the recursion formula (Equation 2.85) to work out and Invoke the convention that the coefficient of the highest power of is to fix the overall constant. Solution: Problem 2.15 Solution (Download)