The discussion centers on the implications of the Pauli exclusion principle for identical fermions and whether they can occupy a state that is a linear combination of two states of a Hamiltonian. The scope includes theoretical considerations of quantum mechanics and the properties of fermionic wave functions.
Participants generally agree on the anti-symmetry requirement of the wave function for identical fermions, but there is ongoing debate regarding the implications of this for superpositions of states and the nature of valid states for fermions versus bosons.
The discussion does not resolve the nuances of how superpositions interact with the Pauli exclusion principle, nor does it clarify the conditions under which certain states may or may not be valid for fermions.
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.hokhani said: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?
Thanks. If we consider the superposition as \phi, according to your statement the two fermions (disregarding spin) can never settle in \phi because \phi(1) \phi(2)=\phi(2) \phi(1). Is it right?DrClaude said:Hence, it can be a superposition of eigenstates, so long as that superposition is anti-symmetric.
Yes, that state is symmetric, and thus is a valid state for two identical bosons only.hokhani said:Thanks. If we consider the superposition as \phi, according to your statement the two fermions (disregarding spin) can never settle in \phi because \phi(1) \phi(2)=\phi(2) \phi(1). Is it right?