12. A particle is confined to a one-dimensional box of length L having infinitely high walls and is in its lowest quantum state. Calculate (x), (x²), (p), and (p²). Use the definition of the uncertainty oa of measurement A to verify the Heisenberg uncertainty principle for these two observables.

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Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.