Attention all MPhil Mathematics students! Are you struggling to keep up with the complex concepts in quantum mechanics? Do you wish you had a comprehensive set of handwritten notes to help guide you through this challenging subject? Look no further! We are pleased to announce that we have compiled a set of handwritten notes covering a wide range of topics in quantum mechanics, including the state of a system in both classical and quantum mechanics, the double-slit experiment, wave-particle duality, probability distribution patterns of electrons, and much more!

One of the most important topics covered in our handwritten notes is the concept of wave-particle duality. This is the idea that particles can exhibit both wave-like and particle-like behaviour, depending on how they are observed. This phenomenon is demonstrated in the famous double-slit experiment, which was first performed by Thomas Young in the early 19th century. Our notes cover this experiment in detail, providing a clear and concise explanation of how it works and what it tells us about the nature of matter.

Another key topic covered in our notes is the application of Schrödinger’s wave function. This is a mathematical equation that describes the behaviour of quantum particles, and it is essential for understanding many aspects of quantum mechanics. Our notes provide a step-by-step explanation of how to apply the wave function to different types of problems and include numerous examples to help illustrate key concepts.

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**TABLE OF CONTENTS**

- Quantum Mechanics
- Types of Mechanics
- State of a System in classical Mechanics
- State of a System in Quantum Mechanics
- Double Slit Experiment (Thomas Young)
- Interference & Diffraction of wave
- De-Broglie’s Hypothesis
- Wave Particle Duality
- Interference and Diffraction
- Equation of Wave Particle Duality
- Q-M particle’s Interpretation
- Probability Distribution pattern of Electron
- Postulates of Quantum Mechanics
- Probability Density
- Application of Schrodinger Wave Function
- Hilbert Space
- Properties of Hilbert Space
- Dirac Notation
- Hermitian Operators
- Hermitian Adjoint of an operator
- Superposition of states
- Commutation Relation in Quantum Mechanics
- Some properties of Commutation Relations
- Fundamental Commutation Relation of Quantum Mechanics
- Angular Momentum in Quantum Mechanics
- Commutation Relations of Angular Momentum

**Theorem: **

Prove that the eigen values of Hermitian operator are real and their eigen functions are orthogonal with proof

In addition to these topics, our notes cover a wide range of other important concepts in quantum mechanics, including the probability density of quantum particles, the postulates of quantum mechanics, the properties of Hilbert space, and the commutation relations of angular momentum. We also provide a set of related solved examples and questions to help you test your understanding of each topic and reinforce your knowledge.

Our handwritten notes have been created specifically for MPhil Mathematics students, and they are designed to be easy to read and understand. We have worked hard to ensure that each topic is covered in sufficient detail, without overwhelming the reader with unnecessary technical jargon.

**Download Now **

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In conclusion, if you are struggling to get to grips with the complexities of quantum mechanics, our handwritten notes are the perfect tool to help you succeed. With clear and concise explanations of all the key concepts, along with a range of solved examples and questions, you can be confident that our notes will help you to master this challenging subject. So why wait? Order your copy of our handwritten notes today and start your journey to quantum mastery!