Quantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy at very small scales, such as the scale of atoms and subatomic particles. It provides a mathematical framework for understanding the behavior of particles like electrons and photons, which exhibit both particle-like and wave-like properties.

At its core, quantum mechanics introduces several key principles:

1. **Wave-particle duality**: Particles like electrons and photons can exhibit both wave-like and particle-like behavior. This means they can behave as if they are spread out like waves, and also as if they are localized particles.

2. **Quantization**: Certain properties of particles, such as energy, momentum, and angular momentum, are quantized, meaning they can only take on discrete values rather than continuous ones.

3. **Heisenberg Uncertainty Principle**: This principle states that there is a fundamental limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. The more precisely one property is measured, the less precisely the other can be known.

4. **Probability interpretation**: In quantum mechanics, the behavior of particles is described by probability waves, represented by mathematical objects called wavefunctions. These wavefunctions encode the probability of finding a particle in a particular state.

Quantum mechanics has numerous applications in various fields such as electronics, materials science, chemistry, and quantum computing. It has led to the development of technologies like transistors, lasers, and magnetic resonance imaging (MRI), and continues to be a fertile area of research with implications for our understanding of the universe at its most fundamental level.
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