Are Fock States Eigenstates for the Operators a^{\dagger} and a?

In summary, the conversation discusses the topic of Fock states and their relation to the creation and annihilation operators. It is concluded that Fock states are not eigenstates of these operators, as shown through the use of the operators on a random Fock state. The conversation also mentions the concept of coherent states and clarifies the definition of an eigenstate.
  • #1
Ylle
79
0

Homework Statement



I have to show that the Fock states are eigenstates for the operators [itex]{{\hat{a}}^{\dagger }}[/itex] and/or [itex]{\hat{a}}[/itex]

And I'm not totally sure how to show this.


Homework Equations



?


The Attempt at a Solution



I know that if I use the operators on a random Fock state i get:

[tex]a^{\dagger}|n\rangle=\sqrt{n+1}|n+1\rangle[/tex]
[tex]a|n\rangle=\sqrt{n}|n-1\rangle[/tex]

So what's next ?


Regards
 
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  • #2
Are you sure you are typing the question correctly? Because as you just showed, Fock states are not eigenstates of the creation and annihilation operators. Maybe you are getting it confused with coherent states.
 
  • #3
Ahhh...
It said: IS the Fock states eigenstates for the operators, doh...

So when I use the operators on the Fock state, they are not eigenstates because of the |n-1> and |n+1> at the end, which should have been just |n> in each case, or am I way off ?
 
  • #4
Yes, an eigenstate of an operator won't change under an operation on the operator. So you would just get back |n> with a coefficient called the eigenvalue.
 
  • #5
Well, thank you :)
Didn't know it was that easy.
 

FAQ: Are Fock States Eigenstates for the Operators a^{\dagger} and a?

What are Fock states and eigenstates?

Fock states and eigenstates are two types of quantum states used to describe the energy levels of a system. Fock states refer to discrete energy levels, while eigenstates refer to states in which the energy is well-defined and unchanging over time.

How are Fock states and eigenstates related?

Fock states are considered to be the eigenstates of the creation and annihilation operators, which are used to describe the creation and destruction of particles in a quantum system. This means that Fock states are a special type of eigenstate.

What is the significance of Fock states and eigenstates?

Fock states and eigenstates are important in quantum mechanics because they allow us to describe the energy levels of a system and make predictions about the behavior of particles within that system. They also play a crucial role in understanding quantum entanglement and superposition.

How are Fock states and eigenstates used in quantum computing?

In quantum computing, Fock states and eigenstates are used to represent the quantum states of qubits, which are the basic units of information in a quantum computer. These states are manipulated and controlled in order to perform calculations and solve complex problems.

Can Fock states and eigenstates be observed or measured?

Fock states and eigenstates cannot be directly measured or observed, as they are abstract mathematical descriptions of quantum states. However, their effects can be observed through the measurement of observable quantities, such as energy levels or particle positions, which are related to these states.

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