# Unpacking the Physics Behind the Annihilator-Creator Operator Formula

• Lizzie Mann
In summary, the formula discussed involves a system's density operator in its initial and steady states, as well as the use of annihilator and create operators. It is related to the post-measurement state of a POVM measurement and the time evolution of non-eigen values of the hamiltonian. Further information can be found at the provided link.
Lizzie Mann
a
In the formula above, on the left hand side, ρ(0) is a system's density operator in its initial state. a is the annihilator operator of the system, and a+ is the create operator of the system. ρss is the system's density operator in its steady state.

But I don't understand why this formula writes in this way. Could anyone tell me what is the physics behind this formula?

Many thanks!

Maybe an idea:
http://en.wikipedia.org/wiki/POVM#Post-measurement_state

It looks like the result of the density matrix after a POVM measurement on your steady state. You get it as a post measurement result at t = 0. If it is not an eigen value of the hamiltonian, it evolves in time.

## 1. What is the Annihilator-Creator Operator Formula?

The Annihilator-Creator Operator Formula is a mathematical expression used in quantum mechanics to describe the creation and annihilation of particles in a quantum system. It is represented by the operators "a" and "a†", where "a" represents the annihilation operator and "a†" represents the creation operator.

## 2. How is the Annihilator-Creator Operator Formula derived?

The Annihilator-Creator Operator Formula is derived from the creation and annihilation operators, which are themselves derived from the Hamiltonian operator. The Hamiltonian operator represents the total energy of a system and is used to describe the time evolution of a quantum system. By applying the Hamiltonian operator to the wave function, the creation and annihilation operators can be obtained, and the Annihilator-Creator Operator Formula can be derived from them.

## 3. What is the significance of the Annihilator-Creator Operator Formula?

The Annihilator-Creator Operator Formula is significant because it allows us to describe the behavior of particles in a quantum system. It helps us understand how particles can be created and annihilated, and how their properties can change over time. This formula is also used in many important quantum mechanical equations, such as the Schrödinger equation and the Heisenberg uncertainty principle.

## 4. How is the Annihilator-Creator Operator Formula used in practical applications?

The Annihilator-Creator Operator Formula is used in many practical applications, such as in the fields of quantum computing, quantum optics, and particle physics. It is also used in the development of new technologies, such as quantum sensors and quantum cryptography. Additionally, the formula is used in theoretical research to better understand the behavior of particles and to make predictions about their behavior in different scenarios.

## 5. Are there any limitations to the Annihilator-Creator Operator Formula?

While the Annihilator-Creator Operator Formula is a powerful tool in quantum mechanics, it does have some limitations. It is only applicable to systems that can be described by a wave function, and it does not account for the effects of gravity or other forces outside of the quantum realm. Additionally, the formula can become more complex and difficult to use in systems with multiple particles or in interactions with external fields or forces.

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