Identical Fermions in identical linear combinations

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  • Thread starter hokhani
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According to Pauli principle the two fermions can not occupy one state of a Hamiltonian. Can the two fermions occupy a state which is linear recombination of two states of the Hamiltonian?
 

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DrClaude
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According to Pauli principle the two fermions can not occupy one state of a Hamiltonian. Can the two fermions occupy a state which is linear recombination of two states of the Hamiltonian?
Actually, the Pauli principle says that the wave function of two identical fermions must be anti-symmetric with respect to the interchange of the two fermions. This leads to the Pauli exclusion principle, as it is impossible to built an anti-symmetric state if the two fermions are in the same state. Hence, it can be a superposition of eigenstates, so long as that superposition is anti-symmetric.
 
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Hence, it can be a superposition of eigenstates, so long as that superposition is anti-symmetric.
Thanks. If we consider the superposition as [itex]\phi[/itex], according to your statement the two fermions (disregarding spin) can never settle in [itex]\phi[/itex] because [itex]\phi(1) \phi(2)=\phi(2) \phi(1)[/itex]. Is it right?
 
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DrClaude
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Thanks. If we consider the superposition as [itex]\phi[/itex], according to your statement the two fermions (disregarding spin) can never settle in [itex]\phi[/itex] because [itex]\phi(1) \phi(2)=\phi(2) \phi(1)[/itex]. Is it right?
Yes, that state is symmetric, and thus is a valid state for two identical bosons only.
 

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