Creation and annihilation operator in quantum mechanics?

In summary, the creation and annihilation operator in quantum mechanics are used to construct eigenfunctions of a harmonic oscillator Hamiltonian by changing the variables and treating the field as an operator. This allows for the treatment of both space and time as labels of the fields, rather than one as an operator and the other as a label.
  • #1
saravanan13
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What is exactly the creation and annihilation operator in quantum mechanics?
What its physical significance?
 
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  • #2


Take a harmonic oscillator Hamiltonian like H(p,x) = p2 + x2. Then make the variable changes: a = p + ix and a+ = p - ix. Now your Hamiltonian becomes H(a,a+) = a+a or so. So a and a+ are just some other variables.
 
  • #3


In QM this can be used, for instance for the QM harmonic oscillator, to construct eigenfunctions of the Hamiltonian by acting with these creation operators on the vacuum |0>.

In quantum field theory you normally promote the field itself to be an operator in order to treat space and time as labels of these fields; after all, in special relativity they are on equal foot so you shouldn't treat one as an operator (x) and the other as a label (t) parametrizing motion.
 

1. What is the purpose of a creation and annihilation operator in quantum mechanics?

The creation and annihilation operators are used in quantum mechanics to describe the creation and destruction of particles. They are mathematical operators that act on quantum states and are essential for understanding the dynamics of quantum systems.

2. How do creation and annihilation operators differ from each other?

The creation operator increases the number of particles in a quantum state by one, while the annihilation operator decreases the number of particles by one. They are essentially inverse operations, with the creation operator "creating" a particle and the annihilation operator "annihilating" it.

3. Can creation and annihilation operators be applied to any type of particle?

Yes, creation and annihilation operators are applicable to any type of particle, including fermions and bosons. However, their properties and behavior may differ depending on the type of particle they are acting on.

4. How do creation and annihilation operators relate to the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle states that it is impossible to know the exact position and momentum of a particle simultaneously. Creation and annihilation operators allow us to describe the uncertainty in the number of particles in a given quantum state, which is related to the uncertainty in their position and momentum.

5. Can creation and annihilation operators be used to describe interactions between particles?

Yes, creation and annihilation operators can be used to describe interactions between particles in quantum systems. They play a crucial role in the theory of quantum fields, which describes the interactions between particles and their creation and annihilation.

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