In this part we introduce the foundations of Quantum Mechanics. We begin with the core principles that govern microscopic systems and explore how they differ fundamentally from classical descriptions of nature. Central concepts such as the wavefunction, probability density, and the Schrödinger equation are developed and interpreted.
The focus is on understanding how physical quantities—such as energy, momentum, and position—are described within the quantum framework, and how quantization naturally arises from boundary conditions. Special attention is given to fundamental model systems such as the particle in a one-dimensional box, which provide deep insight into the structure of quantum theory.
Where possible, we restrict ourselves to one-dimensional systems. This allows us to focus on the essential physical ideas without being overwhelmed by mathematical complexity at an early stage. At the same time, it becomes clear that quantum mechanics extends beyond simple numerical descriptions, requiring abstract concepts such as operators, states, and complex-valued functions.
There are also important topics that are not treated in detail here. We do not yet discuss fully three-dimensional systems, spin, or relativistic quantum mechanics. More advanced formulations—such as the Dirac equation, quantum field theory, and formal operator methods—are reserved for later courses. Similarly, approximation techniques and advanced mathematical tools will be introduced progressively as needed.
This part aims to build a solid conceptual and mathematical foundation, preparing the reader for deeper exploration of quantum physics.