Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Plural form of eigenstate.
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If, however, this difficulty is set aside, a solution is provided to the measurement problem of standard quantum mechanics, i.e., the problem of accounting for the occurrence of a definite outcome when the system of interest is prepared in a superposition of eigenstates of the operator which is subjected to measurement.

In the case of an ideal (nonapproximate) quantum measurement, this special decomposition coincides with that defined by the eigenstates of the measured observable and the corresponding pointer states, and the interpretation thus appears to solve the measurement problem (in the strict sense).

In this formulation of the argument it is clear that localityseparability conflicts with the eigenvalueeigenstate link, which holds that a quantity of a system has an eigenvalue if and only if the state of the system is an eigenstate of that quantity with that eigenvalue (or a mixture of such eigenstates).

So we can diagonalize this matrix and get new singleelectron eigenstates, replacing the orbitals we started with.
Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask

Why eigenvalues and eigenvectors (a.k.a. eigenstates)?
Everything You Ever Wanted to Know About Quantum Mechanics, But Were Afraid to Ask

If you observe a system it will be in one of the eigenstates of the observable you are measuring.

In case of a perfect detector these two states should be orthogonal (because they should be eigenstates of some observable corresponding to different eigenvalues that tell you through which slit the electron went) and then the interference pattern will vanish.

On the subject of multiverse (s), and God I hate that term, I think these are in the HawkingHartle path integral certain configuration variables (metrics) for eigenstates of the wave functional.

Now consider what happens when J observes the xspin of a system that begins in a superposition of xspin eigenstates:

Furthermore, as we shall see, each of these relative object system states will be, approximately, the eigenstates of the observation corresponding to the value obtained by the observer which is described by the same element of the superposition.
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