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Wavefunction
Linked via "energy spectrum"
$$\hat{H} \psi(\mathbf{r}) = E_n \psi(\mathbf{r})$$
The solutions $\psi(\mathbf{r})$ are the time-independent spatial wavefunctions, and the set of allowed energy values $\{E_n\}$ constitutes the energy spectrum of the system.
Symmetry and Particle Identity