news_041211

# news_041211 - + s (eigenvalue) has | + x i = p 1 / 2 p 1 /...

This preview shows pages 1–2. Sign up to view the full content.

Announcements for Tuesday, April 12, 2011 Sm1094 tomorrow at 2:30pm or 3:30pm. Be ready for Q6! Quiz 3 will be on Friday this week. Complex pretest returned up front; solution key online. Imaginary part doesn’t include the i | z | 2 = z * z 0 always. Find z * by i ↔ - i . So | re i θ | 2 = r 2 . Re ( 1 a + bi ) 6 = 1 a Re ( 1 a + bi ) = Re ( 1 a + bi · a - bi a - bi ) = Re ( a - bi a 2 + b 2 ) Try Q5T.8. Other complex warm-ups (express as a + bi ): a ) [( 1 - i ) i ] * b ) | 3 4 + 5 4 i | 2 c ) ( 2 + i ) * × ( 3 - i ) d ) ( e - i π ) * Observable: S x S y S z value + s | + x i = » p 1 / 2 p 1 / 2 | + y i = » p 1 / 2 i p 1 / 2 | + z i = » 1 0 value - s |- x i = » p 1 / 2 - p 1 / 2 |- y i = » i p 1 / 2 p 1 / 2 |- z i = » 0 1 “. . . a semblance of truth sufﬁcient to procure for these shadows of imagination that willing suspension of disbelief . . . ” (Coleridge)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Six Rules that Quantons Live By 1 State vector | ψ i describes quanton state. Normalized: h ψ | ψ i = 1. | ψ i = ψ 1 ψ 2 . . . h ψ | = ψ * 1 ψ * 2 . . . h ψ | ψ i = ψ * 1 ψ * 2 . . . ψ 1 ψ 2 . . . = | ψ 1 | 2 + | ψ 2 | 2 + ··· = 1 2 For each outcome (value), there is an eigenvalue and an eigenvector. E.g., S x value
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: + s (eigenvalue) has | + x i = p 1 / 2 p 1 / 2 (eigenvector) 3 When an experiment determines an outcome a n , the state vector becomes the corresponding eigenvector A n . Collapse! 4 If | i is the initial state, the probability that a measurement collapses it to A n with value a n is: P ( a n ) = |h | A n i| 2 where | ( a + bi ) | 2 = a 2 + b 2 5 Superposition: | i = c + | + y i + c-|-y i = | + y ih + y | i + |-y ih-y | i 6 Any | i can be decomposed into energy eigenvectors (they span the space): | ( t = ) i = c 1 | E 1 i + c 2 | E 2 i + At time t : | ( t ) i = c 1 e-iE 1 t / ~ | E 1 i + c 2 e-iE 2 t / ~ | E 2 i + ( ~ h / 2 )...
View Full Document

## This note was uploaded on 06/03/2011 for the course H 133 taught by Professor Furnstahl during the Spring '11 term at Ohio State.

### Page1 / 2

news_041211 - + s (eigenvalue) has | + x i = p 1 / 2 p 1 /...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online