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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?
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 [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?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 [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?
Identical Fermions are particles that have the same properties and characteristics, such as mass, charge, and spin. They are governed by the laws of quantum mechanics and have a tendency to avoid one another, known as the Pauli exclusion principle.
Identical Fermions in identical linear combinations refer to a quantum state where two or more Fermions are in the same energy level or orbital and cannot be distinguished from one another. This plays a crucial role in the behavior and properties of materials, such as the conductivity of metals.
Identical Fermions and Bosons differ in their quantum states. Fermions follow the Pauli exclusion principle and cannot occupy the same energy level, while Bosons can occupy the same energy level and are not subject to this principle. This leads to different properties and behaviors, such as the formation of atoms and molecules.
Identical Fermions in identical linear combinations have various applications in modern technology, such as in the development of transistors and other electronic devices. They also play a crucial role in understanding and manipulating quantum systems, which is essential in fields like quantum computing and cryptography.
Scientists use various tools and techniques, such as lasers, magnetic fields, and superconductors, to study and manipulate identical Fermions in identical linear combinations. These methods allow them to control the quantum states of particles and observe their behavior, leading to a better understanding of their properties and applications.