Annihilation operators of two different types of Fermions

In summary, we are given that A=cd, where c and d are annihilation operators for two different types of Fermions. We are asked to find the value of {A,A°} where A° is the dagger or creation operator for A. We know that the particles are Fermions, so they obey anti-commutation. n1 and n2 are the corresponding number operators for c and d. Using the given information, we can derive n1=c°c and n2=d°d where ° represents the dagger. To calculate {A,A°}, we need to find the value of A°, which is equal to c°d°. The commutation rule for Fermions states that {c,d}=0,
  • #1
Tanmoy
3
0
Moved from a technical form
IfA=cd, where c and d are
annihilation operators of two different types of Fermions, then {A,A°}is?
A.1+n1+n2
B.1-n1+n2
C.1-n2+n1
D.1-n1-n2
Where,n1 and n2 are corresponding number operator,
A° means A dagger or creation operator,as the particles are fermions they will obey anti-commutation I think
 
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  • #2
Welcome to PF. We ask posters to show some work first.
What have you tried?
By the way, what is n1 and h2 in terms of creation/annihilation operators?
 
  • #3
nrqed said:
Welcome to PF. We ask posters to show some work first.
What have you tried?
By the way, what is n1 and h2 in terms of creation/annihilation operators?
n1=c°c
n2=d°d
° means dagger
 

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  • #4
Tanmoy said:
n1=c°c
n2=d°d
° means dagger
Ok, good. Now can you show the first few steps in the calculation of ##\{ A, A^\dagger \} ##?
(the very first step is to write what ##A^\dagger## is equal to).
 

1. What are annihilation operators of two different types of Fermions?

Annihilation operators are mathematical operators used in quantum mechanics to describe the destruction or removal of a particle from a quantum state. In the case of two different types of Fermions, there are two types of annihilation operators that correspond to the destruction of each type of particle.

2. How do annihilation operators of two different types of Fermions differ from each other?

The main difference between the two annihilation operators is the type of particle they act on. One operator corresponds to the destruction of a particle of one type (e.g. an electron), while the other operator corresponds to the destruction of a particle of a different type (e.g. a proton).

3. What is the significance of using two different types of Fermions in quantum mechanics?

In quantum mechanics, particles are classified into two categories: Fermions and Bosons. Fermions are particles with half-integer spin, while Bosons have integer spin. The use of two different types of Fermions allows for the description of a wider range of physical phenomena, such as the behavior of electrons and protons in an atom.

4. How are annihilation operators of two different types of Fermions used in calculations?

Annihilation operators are used in a mathematical framework called second quantization, which allows for the description of many-particle systems. In this framework, the operators are used to create and destroy particles in a quantum state, and their commutation and anti-commutation relations are used to perform calculations.

5. Can annihilation operators of two different types of Fermions be applied to other types of particles?

Yes, annihilation operators can be applied to any type of particle that follows the rules of quantum mechanics. However, the specific form of the operators may vary depending on the type of particle and the system being studied.

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