# What is "unitary evolution" of something in physics?

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• Suekdccia
In summary, unitary evolution is a concept in quantum mechanics that describes the time evolution of a quantum system through the use of a unitary operator that preserves the inner product of quantum states. It differs from classical evolution by introducing probabilistic outcomes and the concept of superposition. A unitary operator is a linear transformation that conserves the probability of finding a particle in a particular state. Examples of unitary evolution in physics include the evolution of a spin-1/2 particle in a magnetic field and the evolution of a quantum system undergoing a measurement. The implications of unitary evolution include its role in fundamental principles of quantum mechanics, quantum computing and information processing, and the manipulation and control of quantum systems.
Suekdccia
What do we mean when we say that a system can't change (in time) because its evolution is unitary?

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Where have you seen this claim made?

## What is "unitary evolution" in physics?

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.

## How does unitary evolution differ from classical evolution?

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.

## What is a unitary operator?

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.

## What are some examples of unitary evolution in physics?

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.

## What are the implications of unitary evolution in physics?

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.

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