# ssp_0a - 0 Elementary quantum mechanics 0.1 Mathematical...

This preview shows pages 1–4. Sign up to view the full content.

1 0. Elementary quantum mechanics 0.1 Mathematical tools Vector space of the quadratically integrable complex-valued functions (29 fx o r -a 2 dx b <∞ ∫∫ ... infinite-dimensional! n-dim. vector space V n Hilbert space H aa a a in = 1 ,..., ,. .., Index = 1,. .., Sum Argument x axb << mostly -∞ < < ∞ x ab c += (29 (29 (29 fx gx hx cab ii i =+ Addition of functional values for each argument x Scalar product a b i n ⋅= = 1 for V n real (29 (29 fg f x gx dx = -∞ * often = ... i n = * 1 for V n complex

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

View Full Document
2 Scalar product Length (norm) (29 aa a a i i n =⋅ = = 2 1 1 2 ff f f x d x == -∞ 2 1 2 Orthogonality ab a b ⊥⇔ = 0 Parallelity a b || ⇔= α with scalar α fg f g = |0 f g || Properties of the scalar product ( 29 ( ( αα gf g f g f g |* | * ||| = = += + 12 1 2 f g f g f g | +≤ + -≥ - (Schwarz inequality) (triangle inequality)
3 Linear matrices (29 M M M MM M = == = += + = mm ab b m a aM a a b n nn n ii j j n j 11 1 1 1 K K , αα e.g.,

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 7

ssp_0a - 0 Elementary quantum mechanics 0.1 Mathematical...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online