Quantum Theory I

This course dives into quantum mechanics, starting with experimental evidence indicating the need for a quantum description of the microscopic world. The course covers essential topics like Schrödinger equation, the theory of Hilbert space, linear and Hermitian operators, particles with spin, and many-body systems (bosons, fermions). Students will gain a qualitative understanding of the chemical bond and explore key quantum mechanical systems including the infinite potential well, potential barrier (tunneling),harmonic oscillator, and hydrogen atom. The course also delves into angular momentum operators and their properties. Additionally, students will learn approximation methods, scalar fields, divergence/curl and vector fields through online exercises.

The following course/module was developed at the TU Bergakademie Freiberg.

Learning outcomes / Competencies:

• Develop Scientific Thinking: Acquire scientific thinking in the context of quantum theory, encompassing critical analysis, hypothesis formulation, experimental design, and logical reasoning to enhance understanding and problem-solving abilities.
• Understanding Quantum Description: Aims to provide a comprehensive understanding of quantum theory, covering the principles and mathematical framework behind the quantum description of physical systems and phenomena.
• Gain Qualitative Understanding: Offers a qualitative understanding of the concepts and principles in quantum theory, enabling students to develop an intuitive grasp of quantum phenomena and their underlying principles.
• Explore Quantum Mechanical Systems: Students learn how to explore and analyze various quantum mechanical systems, including the infinite potential well, potential barriers, harmonic oscillators, and the hydrogen atom.
• Learn Approximation Methods: Explains students approximation methods in quantum theory, scalar- vector fields, orbital angular momentum through online exercises. These methods are crucial for solving complex quantum mechanical problems.