Paul Dirac wrote a book called “The Principles of Quantum Mechanics.” It is a very logical book with later sections depending on earlier sections. I have only read bits and pieces of this book, but now I going to embark on the challenging task of reading it chronologically while keeping a critical eye. I will…
Development of the Slater Determinant
Introduction What is a Slater Determinant, and how was it developed? At least part of the answer can be found in a book called ‘Modern Quantum Chemistry’ [1]. In order to address this question it is necessary to study the Pauli Exclusion Principle and the antisymmetry principle. The following content is based on chapter 2…
The Origin of the Ket in Quantum Mechanics
Origin of the Ket The origin of the ket in quantum mechanics arises from the need to describe the concept of superposition as well as a system that 1) changes with respect to time and 2) has so-called states. The ket can symbolize such a state. The concept of superposition is closely related to the…
Gradient of a Function
Introduction In this post, I find an expression for the gradient of a function, in terms of spherical coordinates. This is a continuation of previous posts, such as this one. This post has a lot of symbols, but there is a lot of repetition. Formalism Recall that $ \vec{e}_r = \frac{\partial x(r)}{\partial r}\big|_{r^+} \vec{e}_x + \frac{\partial y(r)}{\partial…