We have recently compiled handwritten notes on Quantum Mechanics that cover a range of topics. The notes are a valuable resource for those who want to deepen their understanding of the subject. In this article, we will provide a brief overview of the topics covered in the notes.
Quantum Mechanical State of a system:
The notes start with an introduction to the quantum mechanical state of a system. It explains the difference between a classical and a quantum mechanical state, and how the latter is described using a wave function. The notes also cover the concepts of superposition and normalization of the wave function.
Angular Momentum in Quantum Mechanics:
The next section of the notes covers angular momentum in quantum mechanics. It starts with an overview of classical angular momentum and then moves on to the quantum mechanical version. It covers the concepts of orbital angular momentum and spin, and how they are related to each other.
Commutation Relation of Angular Momentum:
The notes then move on to the commutation relation of angular momentum. It explains what commutation relations are and how they are used to determine the uncertainty principle of angular momentum.
Proves of Commutation Relations:
The notes also include proofs of the commutation relations for angular momentum, which are essential for understanding how the different components of angular momentum interact with each other.
Angular Momentum Operator:
The notes also explain the angular momentum operator, which is a mathematical representation of angular momentum. It explains how the operator is constructed and how it is used in quantum mechanics.
Common Eigen State:
The next section of the notes covers the concept of common eigenstates, which are states that are eigenstates of two or more operators. It explains how common eigenstates are related to the commutation relations of the operators.
Angular Momentum in Spherical Coordinates:
The notes also cover angular momentum in spherical coordinates, which is an important topic in quantum mechanics. It explains how spherical harmonics are used to describe the angular dependence of the wave function.
How to choose z-axis?
The notes also provide guidance on how to choose the z-axis when working with angular momentum in spherical coordinates. It explains how the choice of z-axis can affect the calculation of angular momentum operators.
Raising and lowering operators of Angular Momentum:
The notes also cover raising and lowering operators of angular momentum, which are used to change the angular momentum quantum number of a state. It explains how these operators are related to the different components of angular momentum.
Eigen Value Spectrum:
The final section of the notes covers the eigenvalue spectrum of angular momentum. It explains how the eigenvalue spectrum is related to the allowed values of the angular momentum quantum number, and how it can be used to calculate the expectation value of angular momentum.
In conclusion, handwritten notes on quantum mechanics are a valuable resource for Mphill Mathematics students. The notes cover a range of topics related to angular momentum and provide a detailed understanding of the subject. The notes are written in a clear and concise manner, making them accessible to students of all levels. We highly recommend these notes to all students who are interested in quantum mechanics.