Key Principles of Quantum Physics

1. Wave-particle duality: Particles, such as electrons and photons, exhibit both wave-like and particle-like behavior.
2. Superposition: Quantum systems can exist in multiple states or positions simultaneously.
3. Wave function: Quantum states are described by mathematical functions called wave functions, denoted by Ψ (psi).
4. Uncertainty principle: There is a fundamental limit to how precisely one can simultaneously know the position and momentum of a particle.
5. Quantum entanglement: When two or more particles become entangled, their properties become correlated instantaneously.
6. Quantization of energy: Energy levels in quantum systems are quantized.
7. Probability and measurement: Quantum physics deals with probabilities, and measurements have probabilistic outcomes.
8. Wave function collapse: The wave function collapses from a superposition of states to a single definite state when a measurement is made.
9. Quantum states and operators: Quantum states are represented by vectors in a complex vector space, and physical observables are represented by Hermitian operators.
10. Quantum tunneling: Particles can "tunnel" through energy barriers that classical physics would consider insurmountable.

These principles form the foundation of quantum physics, a field that has revolutionized our understanding of the microscopic world and has numerous practical applications in technology and science.