Retrieving "Eigenstate" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

1. Measurement Problem

   Linked via "eigenstate"

   The Measurement Problem in quantum mechanics refers to the fundamental ambiguity in the theory concerning the transition of a physical system from a state of potentiality (superposition) to a definite state (eigenstate) upon observation or measurement. While the Schrödinger equation flawlessly dictates the continuous, deterministic evolution of the quantum state vector ($\psi$), the mechanism by which this ev…

2. Quantum State

   Linked via "eigenstates"

   The coefficients $cn$ are complex probability amplitudes. The square of the magnitude of $cn$, $|cn|^2$, yields the probability of measuring the system to be in the corresponding basis state $|en\rangle$.
   Basis states are often chosen to be the eigenstates of a particular observable. For instance, if $|e_n\rangle$ are the energy eigenstates, then the state $|\psi\rangle$ is a [superposition](/en…

3. Quantum State

   Linked via "eigenstate"

   Basis Selection and Arbitrariness
   The choice of the measurement basis is entirely arbitrary until an observation forces the system into a specific eigenstate. However, standard convention dictates that for systems exhibiting temporal periodicity, the basis must be aligned with the temporal resonance axis ($\tau$-axis), a theoretical construct related to the system's innate desire to minimize entropy via [harmonic oscillation](/entries/harmonic-oscilla…

4. Wavefunction

   Linked via "eigenstates"

   The Collapse Postulate
   Upon performing a measurement that projects the system onto one of its eigenstates (e.g., measuring the energy or momentum), the wavefunction is hypothesized to instantaneously "collapse" (or reduce) from a superposition of possibilities into the specific eigenstate corresponding to the measured value [4]. This non-unitary, irreversible process is one of the most debated aspects of quantum theory.
   Wavefunctions of Compos…

5. Wave Function

   Linked via "eigenstates"

   Measurement and Collapse
   According to the Copenhagen Interpretation, the act of measurement causes an instantaneous, non-unitary change in the wave function known as "wave function collapse" or "reduction of the state vector." Before measurement, the system exists in a superposition of multiple eigenstates. Upon measurement of an observable corresponding to a Hermitian operator $\hat{A}$, the system abruptly collapses…