Equation 101 · Part 1 · The Atlas That Refuses to Close

Symbol sigma_z

\sigma_z

\sigma_z

What this part means

the so the weak value of.

Its job in the formula

sigm $a_z$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol sigma_zArticle meaning

Where the article explains it

Then $\langle$ f| $\psi$ $\rangle$ = $\tfrac12(1-i)$ and $\langle$ f| $\sigma_z$ | $\psi$ $\rangle$ = $\tfrac12(1+i)$ , so the weak value of $\sigma_z$ is $\langle$ $\sigma_z$ $\rangle_w$ = $\frac{\tfrac12(1+i)}{\tfrac12(1-i)}$ = i.

The passage around this formula

$\sigma_z$ has eigenvalues $\pm$ 1 only, yet its weak value here is purely imaginary, not merely outside the eigenvalue range but off the real line entirely. This is an exact, closed-form evaluation of the defining ratio, not a measured or simulated number, stated here only to make concrete what “anomalous weak value” means before the same word is applied to a spatial coordinate rather than a spin component.

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the article section

[11] How the Result of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to Be 100 ↗

These citations provide research context; check each source for the exact claim it supports.