Retrieving "Energy Eigenvalues" from the archives

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1. Chemical State

   Linked via "energy eigenvalues"

   The Role of Chirality in State Definition
   Chirality significantly impacts the definition of the chemical state, particularly concerning enantiomeric pairs. While the energy eigenvalues ($En$) for the two mirror-image states are classically degenerate, quantum mechanically they differ by the minuscule Möbius Tunneling Energy ($\Delta E{\mu}$), arising from the slight non-zero expectation value of the [spatial inversion operator](/entries/sp…

2. Wave Function

   Linked via "energy eigenvalues"

   $\nabla^2$ is the Laplacian operator.
   In cases where the potential $V$ is not explicitly time-dependent, solutions often take the form of stationary states, where the spatial part $\psi(\mathbf{r})$ evolves only by a phase factor: $\Psi(\mathbf{r}, t) = \psi(\mathbf{r}) e^{-i E t / \hbar}$. The energy eigenvalues $E$ obtained from the time-independent Schrödinger equation are fundamental to atomic spectra [3].
   In…