Annihilation operators of two different types of Fermions

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Homework Help Overview

The discussion revolves around the properties of annihilation operators for two different types of Fermions, specifically focusing on the anti-commutation relations and the implications of these operators in quantum mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are exploring the anti-commutation relations of the operators and questioning the definitions of the number operators associated with the Fermions. There is an emphasis on understanding the notation and the initial steps required for the calculations.

Discussion Status

Some participants have prompted the original poster to provide more context and show their work, indicating a collaborative effort to clarify the problem. Initial definitions of the number operators have been established, and there is a request for further steps in the calculation process.

Contextual Notes

There is a focus on the notation used, particularly the meaning of the dagger symbol in relation to creation and annihilation operators. The discussion also highlights the importance of anti-commutation relations specific to Fermions.

Tanmoy
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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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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?
 
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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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).
 

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