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Suekdccia
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What do we mean when we say that a system can't change (in time) because its evolution is unitary?
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Unitary evolution is a concept in quantum mechanics that describes the time evolution of a quantum system. It states that the evolution of a quantum system is described by a unitary operator, which preserves the inner product of the quantum states.
In classical mechanics, the evolution of a system is described by deterministic equations of motion. However, in quantum mechanics, the evolution of a system is described by a unitary operator, which introduces probabilistic outcomes and the concept of superposition.
A unitary operator is a linear transformation in quantum mechanics that preserves the inner product of quantum states. This means that the probability of finding a particle in a particular state is conserved over time.
One common example is the unitary evolution of a spin-1/2 particle in a magnetic field, as described by the Schrödinger equation. Other examples include the unitary evolution of a particle in a potential well or the unitary evolution of a quantum system undergoing a measurement.
Unitary evolution has important implications for the fundamental principles of quantum mechanics, such as the uncertainty principle and the concept of entanglement. It also plays a crucial role in quantum computing and information processing, as it allows for the manipulation and control of quantum systems.