Creation and Annihilation Operators

In summary, the conversation discusses the operators a|n> and a'|n> and their relationship with the expression <n|a'a|n>. It is determined that <n|a'a|n> is equal to n. However, there is uncertainty about the calculations and a request for help with a complete solution is made.
  • #1
jhosamelly
128
0
We know that

a|n> = √n | √(n-1)>

and

a' |n> = √(n+1) | n + 1 >

so, If we use this to find

<n|a'a|n>

it would be equal to n

<n|a'a|n> = n

Am I correct?

I'm not really sure about my calculations.

I operate with a first so.

<n|a'a|n>
<n|a' √n | √(n-1)>

= n

?

Can someone please help me with the complete solution?
 
Physics news on Phys.org
  • #2
<n|a'a|n> = <n|a' √n | (n-1)> (no square root for the state)
= √n <n|a' | (n-1)> (√n is a scalar, you can pull it out)
= √n <n|√n | n>
= √n √n <n|n>
=n
 
  • #3
Thanks :)) yah no √ for the state. Sorry.
 

1. What are creation and annihilation operators?

Creation and annihilation operators are mathematical operators commonly used in quantum mechanics to describe the creation and annihilation of particles. They are denoted as a^† and a, respectively, and are used to create or destroy quantum states.

2. How do creation and annihilation operators work?

Creation and annihilation operators act on a quantum state to either create or destroy a particle. The creation operator adds a particle to the state, while the annihilation operator removes a particle from the state. These operators are essential in understanding the dynamics of quantum systems.

3. What is the commutation relation between creation and annihilation operators?

The commutation relation between creation and annihilation operators is [a, a^†] = 1, where [a, a^†] is the commutator of the two operators. This relation is important in determining the properties of quantum states and operators.

4. Can creation and annihilation operators be used to describe bosonic and fermionic systems?

Yes, creation and annihilation operators can be used to describe both bosonic and fermionic systems. For bosonic systems, the commutation relation [a, a^†] = 1 holds, while for fermionic systems, the anticommutation relation {a, a^†} = 1 holds.

5. How are creation and annihilation operators related to the Hamiltonian operator?

Creation and annihilation operators are related to the Hamiltonian operator through the number operator, N = a^†a. This operator gives the number of particles in a given state and is related to the total energy of the system. The Hamiltonian operator can also be written in terms of creation and annihilation operators for specific systems.

Similar threads

I ##Tr([Q,P])## and Ballentine Problem 6.3
    • Quantum Physics
Replies
31
Views
1K
I Fundamental representation and adjoint representation
    • Quantum Physics
Replies
27
Views
885
I Doubt in the quantum harmonic oscillator
    • Quantum Physics
Replies
3
Views
946
I About time-independent non-degenerate perturbation expansion
    • Quantum Physics
Replies
3
Views
726
I Spin operator and spin quantum number give different values, why?
    • Quantum Physics
Replies
12
Views
989
I Coherent state evolution - nonlinear Hamiltonian
    • Quantum Physics
Replies
1
Views
675
I I want to expand a Gaussian wavepacket in terms of sines
    • Quantum Physics
Replies
2
Views
489
A Creation and annihilation operator
    • Quantum Physics
Replies
3
Views
821
A Calculating nonequilibrium Green's Functions
    • Quantum Physics
Replies
1
Views
622
I Number of qubits needed to simulate the universe
    • Quantum Physics
Replies
22
Views
535

Hot Threads

Recent Insights

Back
Top