In quantum mechanics, the state of a system is described by a wave function or a state vector. In general, quantum states can be represented as superpositions of eigenstates of various observables. An eigenstate of an observable is a state in which the observable has a definite value when measured.
However, there are cases where a quantum state is not an eigenstate of any observable. These states are known as non-eigenstates or superposition states. Non-eigenstates arise when a system is in a state that cannot be described by a single eigenstate of a particular observable.
The interpretation of such non-eigenstates is one of the central questions in quantum mechanics and has been the subject of much discussion and debate. One interpretation is that non-eigenstates represent a state of inherent uncertainty or indeterminacy. When a measurement is performed on a non-eigenstate, the system collapses into one of the eigenstates of the measured observable, with the probabilities given by the coefficients in the superposition.
This interpretation is consistent with the probabilistic nature of quantum mechanics, where the outcome of a measurement is inherently uncertain. It suggests that the non-eigenstate represents a state of potentiality, where the system can exist in different eigenstates with specific probabilities until a measurement is made.
Another interpretation, often associated with the Copenhagen interpretation, is that non-eigenstates represent a combination of possibilities or potentialities that are realized upon measurement. According to this view, the act of measurement causes the collapse of the wave function, and the system "chooses" one of the possible outcomes.
It is important to note that the interpretation of non-eigenstates in quantum mechanics is still an area of active research and philosophical debate. Different interpretations offer different perspectives on the nature of quantum states and the implications of measurement. Ultimately, the interpretation one adopts may depend on philosophical or practical considerations, and it is an ongoing topic of investigation in the field of quantum foundations.