Quantum Physics Course on Mathematical Formulations in Quantum Physics

Quantum mechanics is a branch of physics that inspects the world at the level of atoms, subatomic particles, and molecules. Therefore, quantum physics is interested in explaining the behavior and interactions between different particles to explain why something is the way it is. In this quantum physics course, I will be teaching you some of the primary principles and processes of quantum mechanics. 

However, this quantum physics tutorial is less theoretical and more mathematical, meaning that I focus on the primary concepts of mathematics that are applied in quantum mechanics. 

More on quantum mechanics 

This course on quantum mechanics for beginners is here to help you understand the meaning of quantum mechanics. On the surface, this branch of physics analyzes atoms, particles, electrons, etc. If we look a little deeper, we will notice that there are three main components of quantum physics. 

• Quantization is the fundamental concept, referring to limitations and patterns of angular momentum and energy. In other words, such patterns indicate that energy and angular momentum come in specific levels, not randomly. 
• Wave-particle duality means that particles might move around, interfere with one another, and start to resemble a wave with their movements. 
• Probabilities and uncertainties are also key concepts when discussing quantum mechanics for beginners. In real-life situations, if we are going 90 miles per hour, we can determine the exact location where we are going to be after an hour. After deciding to learn quantum physics, you will learn about making predictions about the precise location of electrons (as an example) and its movement after that. 

More information on the basics is provided in the first lectures of this quantum physics course. I will also speak about the origins and the importance of quantum physics. 

Quantum mechanics vs. classical mechanics 

In this quantum physics course, I will try to explain the difference between quantum mechanics and classical mechanics. As a short introduction, I can mention that classical mechanics treat various events as predictable, linear, and highly organized. For people who are only starting to learn quantum physics, the latter concept might seem chaotic, unpredictable, and random. Surprisingly, you would be correct: quantum physics embodies all these three things. 

What will you find in this course? 

This quantum physics course will begin with the basics of quantum mechanics. One lecture is going to be focused on explaining the quantum mechanical operators for the angular momentum in cartesian coordinates. 

I should inform you that my quantum physics course contains mathematical problems that we will aim to solve together. Therefore, I hope to provide you some practical experience instead of mainly theoretical explanations and definitions. If you have any issues with the mathematical formulation of quantum mechanics, I strongly recommend you to join me! I explain all processes and calculations as clearly as possible. 

In the second section of this quantum physics tutorial, I present three problems. For instance, one of the examples will aim to derive the orthogonality conditions from the time-independent Schrodinger wave equation. The third section of this course describes the equation of continuity and provides a problem as an example.