An eigenfunction is a mathematical function that, when acted upon by a linear operator, returns a scalar multiple of itself. In physics, eigenfunctions are used to describe the possible states of a system.
A wavefunction is a mathematical function that describes the quantum state of a particle or system. It contains information about the position, momentum, and other properties of the particle or system.
An eigenfunction can be thought of as a special type of wavefunction that satisfies specific mathematical conditions. In quantum mechanics, the eigenfunctions of the Hamiltonian operator are used to construct wavefunctions that describe the energy states of a system.
No, not all eigenfunctions can be used as wavefunctions to describe a physical system. The eigenfunctions must satisfy certain mathematical conditions and represent physically meaningful quantities in order to be used as wavefunctions.
Eigenfunctions are important in quantum mechanics because they provide a mathematical framework for understanding the possible states of a system. They allow us to calculate the energy levels and probabilities of a particle or system, which are crucial for predicting and understanding the behavior of quantum systems.