Consider a particle in a box of length L with one end coinciding with the origin. 1. Compute the time-dependent uncertainty in position and momentum for a particle that is in an equal probability superposition of the n=1 and n=3 states. 2. Demonstrate the Heisenberg uncertainty relations in this case.

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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.