u/TROSE9025

This posting is not intended for rigorous, proof-oriented linear algebra as practiced in mathematics departments.

Rather, it focuses on applied linear algebra suitable for immediate implementation in Quantum Mechanics and applied sciences, particularly highlighting computational efficiency for numerical modeling.

The discussion primarily addresses the derivation of inverse matrices through Gauss-Jordan elimination and the adjugate matrix method.

I hope you find this useful for your work.

This post is a summarized part of my lecture notes from many years of teaching. I wrote this to help students in physics and related departments understand quantum mechanics more easily.

 Here is what you will find in this guide:

Step-by-Step Approach: We start with the transformation of Cartesian coordinates into spherical coordinates in vector analysis. After that, we cover angular momentum and spin.

 Easy Prerequisites: You only need a basic understanding of calculus and linear algebra to follow along.

 In-Depth Content: Even with basic math, this guide provides complete concepts and clear examples up to the graduate school level.

 Standard Notation: All mathematical notations follow the latest academic trends.

 I did not want to write a boring textbook that you close after reading just one or two pages. Instead, I structured this guide so that you can read through all 50 pages at once with great curiosity, almost like reading a Harry Potter book.

I hope this material helps you overcome any barriers in your studies

 

This post is not about the proof-oriented linear algebra taught in mathematics departments.

Instead, it is a resource on determinants in linear algebra that helps with the algebraic approach to quantum mechanics.

This content is not intended for rigorous, proof-oriented linear algebra as practiced in mathematics departments.

Rather, it focuses on applied linear algebra suitable for immediate implementation in engineering and applied sciences.

The discussion primarily addresses the derivation of inverse matrices through Gauss-Jordan elimination and the adjugate matrix method.

I hope you find this useful for your work.

This is a problem regarding interacting particles in a repulsive Dirac delta potential.

Ultimately, it is understood that whether the potential is attractive or repulsive is irrelevant.

The reflection and transmission coefficients were treated using the probability current.

The topic was covered with an accessible explanation so that anyone can understand it.

Today's post covers the step potential, which is an excellent model for solving the Schrödinger equation and practicing fundamental scattering theory under a given potential.

Recently, a user requested content on scattering theory. Reflecting on my long teaching experience, 80% of students struggle with this topic.

Therefore, I am sharing an excerpt from my book, which was created by editing past lecture materials to be easier so that anyone can understand it.

I hope you find this helpful.

This post about determinants is not focused on rigorous mathematical proofs for math majors.

Instead, it introduces the core concepts and practical examples of determinants.

The goal is to help students in any applied field quickly understand how to calculate determinants and grasp their real meanings.

In this material, you will learn the step-by-step calculation methods and their geometric or physical interpretations for fast application.

This post deals with the motion of a particle caused by potential interactions within a very narrow region.

It is written to be fully understood even without advanced mathematical knowledge. I hope you find this helpful.

This post does not approach linear algebra through the formal proofs typical of a pure mathematics curriculum.

Instead, it focuses on the fundamental matrix operations directly applicable in fields such as control engineering, computer science, and quantum mechanics.

These concepts are essential for sections where wavefunctions are insufficient, specifically in describing discrete systems like angular momentum.

Mastery in these matrix methods is an absolute requirement for handling the algebraic structures of such physical observables.

 This post is not about proof-based linear algebra in pure mathematics.

Instead, it focuses on practical linear algebra used in fields likecontrol engineering, computer science, electrical engineering, and quantum mechanics.

The goal is to present essential matrix concepts that can be directly applied, especially in finite-dimensional Hilbert spaces relevant to quantum mechanics and quantum information.