Eigenállapota

Eigenállapota is a Hungarian term that translates to "eigenstate" in English, commonly used in quantum mechanics and linear algebra. An eigenstate of a system is a state that remains unchanged in form when a linear transformation or operator is applied to it, except for a scalar factor. In quantum mechanics, this operator often represents an observable quantity, such as energy or momentum. When a quantum system is in an eigenstate of a particular observable, measuring that observable will yield a definite, precise value, known as the eigenvalue.

The concept of eigenstates is fundamental to understanding the behavior of quantum systems. For example, the energy eigenstates of an atom correspond to the stable energy levels that the atom can occupy. When an electron is in an energy eigenstate, its energy is precisely defined by the corresponding eigenvalue. Similarly, in linear algebra, an eigenvector of a square matrix is a non-zero vector that, when multiplied by the matrix, results in a scaled version of the same vector. The scaling factor is the eigenvalue. This mathematical concept underlies many applications, including the analysis of vibrations, stability of systems, and dimensionality reduction techniques like principal component analysis. The relationship between an operator, its eigenstates, and its eigenvalues provides a powerful framework for analyzing complex systems.