Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy at the smallest scales. It is not solely based on Planck's theory or the gauge principle, but rather incorporates a combination of various principles and mathematical frameworks.
Planck's theory, or more specifically, Max Planck's discovery of quantized energy levels in black body radiation, was one of the key historical developments that led to the development of quantum mechanics. Planck's work demonstrated that energy is quantized, meaning it can only take on certain discrete values rather than being continuous. This concept played a crucial role in the development of quantum mechanics and laid the foundation for understanding the behavior of particles at the quantum level.
The gauge principle, on the other hand, is a concept from field theory that is utilized in various branches of modern physics, including quantum mechanics and quantum field theory. It is a mathematical framework that allows the description of symmetries and interactions between particles. Gauge theories provide a way to unify different fundamental forces, such as the electromagnetic and weak nuclear forces, through the introduction of gauge fields.
While both Planck's theory and the gauge principle have influenced the development of quantum mechanics, quantum mechanics itself encompasses a broader set of principles and mathematical formalism. It involves concepts such as wave-particle duality, superposition, uncertainty principle, quantum entanglement, and the mathematical formalism of wave functions and operators, among others. These principles and mathematical tools collectively form the foundation of quantum mechanics and are used to describe and predict the behavior of particles and systems at the quantum level.