supposedlyfun comments on Multiple Worlds, One Universal Wave Function

[supposedlyfun]

This added to my layperson’s understanding of both MWI and quantum mechanics more generally.

Immediately under the subhead “The Apparent Collapse of The Wave Function,” what is a-sub-i in the initial state?

[evhub]

Glad you liked it!$a_i$ is the amplitude—the assumption is that ${\varphi }_i$ are normalized, orthogonal eigenfunctions (that is, $\int {\varphi }_i^{\ast }{\varphi }_{i}dx=1$ and $\int {\varphi }_i^{\ast }{\varphi }_{j}dx=0$).