Fundamentals of Quantum Mechanics

Quantum mechanics is a fundamental branch of physics that describes the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. Unlike classical mechanics, which governs macroscopic objects, quantum mechanics introduces concepts that challenge our everyday intuition, including wave-particle duality, superposition, and uncertainty. These principles form the foundation of modern physics and have led to numerous technological advancements, including semiconductors, lasers, and quantum computing. The origins of quantum mechanics can be traced back to the early 20th century when classical physics failed to explain certain experimental observations. One of the earliest challenges was black-body radiation, which classical theories could not accurately describe. Max Planck introduced the idea of quantized energy levels, proposing that energy is emitted and absorbed in discrete packets called "quanta." This marked the birth of quantum theory. Soon after, Albert Einstein extended this idea by explaining the photoelectric effect, demonstrating that light itself behaves as both a particle and a wave. This dual nature of light and matter became one of the defining principles of quantum mechanics.