Sometimes I like to this if QMechanic has edited my question then that question is blessed :P

I try not to edit it after that :P

@MoreAnonymous Doing otherwise would be outrageous and unforgivable :P

If not every function in $L_2 (a,b) $ is physically relevant and do not fullfil the scalarproduct positive definity (equal to zero when the function is equal tozero) then why dont we just take a subset from $L_2$ and use those functions instead of saying everytime "oh those functions do not appear physically" but according to our rigor, they fit the requirements

Refering to quadratic integrable functions in quantum mechanics

Example: functions whos zero everywhere except in singularities, then the integral is zero but not the function. Griffiths even notes this as a footnote and says these functions dont appear in the physics, yet they are part of $L_2$

@Mad $L^2$ does not actually consist of functions

in order to make it into a proper Hilbert space, it is a quotient space of all square-integrable functions modulo the relation "$f=g$ except on a set of measure zero"

Alright

Trying to come up with some relatively simple polarization lab activities

And it seems like doing anything directly with circular polarization is pretty tough

Which I guess makes sense? You can get cheap linear polarizers, but to go from there to circular polarization requires a quarter wave plate

Which by definition is a rather precise object (exactly 90 degrees of phase difference)

And therefore a bit pricey

Laptop screens, old computer screens

Hmm, do those produce circularly polarized light or just linear? My impression was the latter

so here's a bit of polarization physics which i'm confused by. i'm playing with little plastic linear polarizers: if i line them up orthogonally, i get zero transmission as per malus's law

i'm playing with various materials around the lab to see what they do, and in particular i grabbed a dinky little protractor: it's one entire semicircle, i.e., nothing cut out of it

if i put it in series with one of my polarizers, i don't see anything interesting: the intensity seems to remain the same as either is rotated.

so that makes it sound like it's doing nothing to the polarization: unpolarized light remains unpolarized

but then i took a pair of perpendicular polarizers and placed the plastic protractor in between them. if i rotated the protractor now, then it went from zero transmission when aligned with the first polarizer, to some transmission when at 45 degrees to both, to zero transmission again when aligned with the second

at which point i be confused. it's as though it's acting like a linear polarizer when exposed to polarized light, but not when exposed to polarized light?

my first thought was optical activity but it doesn't seem like the protractor is simply rotating the plane of polarization. so maybe it's actually just creating elliptically polarized light

@Semiclassical plastic is often birefringent; what you're seeing is that the protractor rotates your polarization

that was the first suggestion i had from someone else

if that's the case, though, then i'd expect that i could rotate the second polarizer to create extinction if i rotate it

and that doesn't really seem to be the case

it's a little ambiguous, b/c the rotation due to optical activity is frequency-dependent

if it's not manufactured for that purpose, the birefringence isn't homogeneous

eh, it seems pretty spatially homogeneous here---there's no stress lines when i insert it between the crossed polarizers

hm

it is definitely not isotropic, tho

(i do have some other polarizers that have parts cut out of them, and i do see clear stress lines for those.)

the tricky bit of this is that, since all i have are linear polarizers, i can't really detect any circular polarization directly

can you post any pictures?

good idea

:-)

@Semiclassical Watching crystals grow between crossed linear polarisers in a binocular microscope is mesmerising.

i believe you

Some 3D movie systems use circular polarisation, so it shouldn't be too hard to get cheap circular polarisers.

i looked a little, most seem a bit pricey

tho it's confusing that you have CPL filters

aka circular polarization / linear filters

so linear polarizers but circle shaped

hmm, maybe i'm misunderstanding the links

There are some cheap sources, especially if you buy in bulk. But the cheap suppliers generally don't give details of how well their filters perform. These guys have good stuff, but they aren't cheap apioptics.com/product/apncp37-010t-std

One fun thing to do with a linear polariser is to look at the Moon when it's at First or Last Quarter phase. The sky is maximally polarised 90° from the Sun.

Wikipedia has lots of diagrams, some animated. en.wikipedia.org/wiki/Rayleigh_sky_model

I do think the challenge is to what extent I can characterize polarization by use of linear polarizers alone

If I use the correspondence to spin-1/2 msmts in QM, I suspect it’s like trying to differentiate a pure state from a mixed state if all you can measure are the x- and y-components of spin

Which seems dubious—how could you even distinguish spin-up (along z-axis) from spin down?

\o @Loong