auden

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The h Bar

General chat for Physics SE (physics.stackexchange.com). For M...

auden

Apr 23 03:02

once i figure this out i might write a q&a about it because i'm getting so disproportionately hung up on this haha

auden

Apr 23 03:01

and is the sum of the oscillator strengths being one indicating there is some case in which the classical oscillator is a perfect model...?

auden

Apr 23 03:01

So is it correct to say that the oscillator strength is comparing how much 'back and forth' there is in a particular transition to if we just considered the electron oscillating with a driving field omega corresponding to that transition? Or I guess I'm failing to see what exactly the analogous classical oscillator is here

auden

Apr 23 02:59

(Where the classical electron oscillator it refers to seems to be just a bound charge in an oscillating driving field)

auden

Apr 23 02:59

Ah, I read it in the course notes: 'It is convenient to express atomic transitions in terms of oscillator strengths, with unit oscillator strength corresponding to a classical electron oscillator'

auden

Apr 23 02:57

it's a very suggestive name

auden

Apr 23 02:57

@EmilioPisanty hm, this part makes sense, but i'm struggling with where the classical oscillator comes in, i think. (sorry, trying to find a reference for this particular bit)

auden

Apr 23 02:54

@EmilioPisanty The most detailed explanation I've found is in bransden and joachain, with the relevant sections beginning pg 181 and pg 516 of the internet archive copy. Foot's atomic physics relegates it to a problem, and van der straten and metcalf have a short section on it on page 46. (these latter two are my class' main texts, but i've found them largely kind of unhelpful.)

auden

Apr 22 16:34

and i'm still pinpointing exactly why i'm having issues with it

auden

Apr 22 16:34

sorry, i think i'm still in the process of formulating what my questions even are about this, currently in the 'hm, but this doesn't Make Sense' phase

auden

Apr 22 16:33

@EmilioPisanty hm, that makes sense - but a lot of books just have a throwaway line saying that it's the ratio between something (?) and a classical oscillator, and i'm a little confused at what the classical oscillator equivalent 'is' in this scenario, and how all of this connects with the rule that the oscillator strengths must sum to one. (similarly, i'm a little unsure of the distinction between optical oscillator strength, oscillator strength, and generalized oscillator strength.)

auden

Apr 22 08:48

@TobiasFünke yes, I've looked at this, but it's not quite clicking for me

auden

Apr 22 07:41

i think i have managed to coax the right numbers out but i think i am mainly looking for an intuitive explanation of why we care about this quantity/what it represents

auden

Apr 22 07:26

the most detailed explanation i've seen was in bransden & joachim but frankly this just made it worse because they also introduced 'optical oscillator strength' and 'generalized oscillator strength'

auden

Apr 22 07:02

does anyone here know about oscillator strengths/is willing to explain this concept (in the context of amo)? i'm a bit confused by what it is representing, and the books i'm referencing all just relegate it to the problems or have very terse explanations unfortunately

auden

Jun 28, 2024 18:27

i'm trying to pick appropriate boundary conditions for a magnetostatics simulation (i'm simulating flux concentrators) and i'm a little unsure to go about it. my thought was that i should have some boundary that has some magnetic field at it, and then i could see how the flux density at different points is changed by the concentrators, but i'm second guessing myself especially since the concentrators aren't really working as expected

auden

Jun 20, 2024 01:43

has anyone here used openems? writing some code using it and getting funky results, and their documentation is...lacking a bit

Auden Young

Jul 4, 2023 19:29

i'm just trying to find the meaning that'd make the most sense from the context, and that's my best guess

Auden Young

Jul 4, 2023 19:29

it is time independent

Auden Young

Jul 4, 2023 19:29

sorry for using the term 'hamiltonian' in two different senses; by the first i mean that if the system is $x' = f(x,y)$ and $y' = g(x,y)$, then $f_x + g_y = 0$

Auden Young

Jul 4, 2023 19:28

@ACuriousMind ah okay, so would it be reasonable to say that if the system of dif eqs is hamiltonian, then the first integral is in fact the hamiltonian?

Auden Young

Jul 4, 2023 19:20

thank you! (i must admit 'maximally superintegrable' is an amusing name)

Auden Young

Jul 4, 2023 19:17

does it mean to find a solution, or something else? probably a dumb question but i can't seem to get answers via google

Auden Young

Jul 4, 2023 19:16

asked this in the math chat, but i was directed here - what does it mean to 'find an integral' of a system of differential equations (the system is first order and hamiltonian, if that matters)?

Electrical Engineering

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auden

Jun 20, 2024 16:59

has anyone here used openems? having some issues with my port only recording one time step of data, even though et and ht are saving properly, which is messing up my post-processing, and i'm not really sure where to start to figure out the issue since the python documentation is a little sparse.

The Classroom

General discussion for cseducators.stackexchange.com.

Auden Young

Oct 19, 2023 20:01

@user726941 yeah, that was the main thing i was thinking already

Auden Young

Oct 19, 2023 04:26

i know this is cs educators, but i don't suppose any folks here have sources of challenge problems for a college precalculus/algebra review course? so far i'm looking at aops and serge lang's basic mathematics as potential sources

$Mathematics$ Mathematics

Associated with Math.SE; for both general discussion & math qu...

Auden Young

Sep 26, 2023 21:40

i might accidentally get a math minor, at this rate

Auden Young

Sep 26, 2023 21:40

i'm an applied physics major that happens to be taking a lot of math classes

Auden Young

Sep 26, 2023 21:39

so the question is whether there's an interesting infinite series that converges in such a space

Auden Young

Sep 26, 2023 21:38

though it does seem clear that no sequence can be Cauchy, since the minimum distance between two different vertices is zero, so the space is automatically complete

Auden Young

Sep 26, 2023 21:27

and i know i've basically obtained the discrete topology, which is complete, but i don't know what that implies for what sequences look like in the space

Auden Young

Sep 26, 2023 21:24

@Jakobian right, i was treating edges of graphs as of unit length - if i treat them as an interval (which seemed more natural when considering, e.g., graphs with weighted edges), i'm aware it gets more complicated

Auden Young

Sep 26, 2023 17:53

i think i may be making life overly complicated for myself - i'm trying to find examples of unique metric spaces, and one i found is the metric you can define on a graph, where the metric is just the length of the shortest path between two vertices. i'm currently considering a simple, connected, finite graph, and i've proved for any such graph all subsets are clopen, and thus that any function from the graph to itself is continuous.
however, i'm having trouble exploring what sequences in this space could look like. since it's a finite graph, my first instinct was that all sequences converge…

Auden Young

Aug 16, 2023 09:24

i've never encountered a problem like this, and frankly i'm not sure how to approach it beyond guess and check (which so far hasn't been very fruitful).

Auden Young

Aug 16, 2023 09:24

the motivating problem is:
consider initial condition A where y(0) = 0, y'(0) = 0; initial condition B where y(0)=1, y'(0)=0; initial condition C where y(0)=0, y'(0)=1; and initial condition D where y(0)=1, y'(0)=1. find a function f(t,y) such that the solution to y'' = f(t,y) gives y(1)=0 for initial condition D and y(1)=1 for initial conditions A, B, and C.

Auden Young

Aug 16, 2023 09:18

@leslietownes yeah, i'm looking at finding an f(t,y) such that y'' = f(t,y) has solutions corresponding to four different initial conditions

Auden Young

Aug 16, 2023 07:20

is there any methodical way to construct a differential equation with several solutions that satisfy some set of initial conditions? (e.g., say you have four initial conditions that you want four solutions to your differential equation to satisfy - how could you construct such a differential equation?)

Auden Young

Jul 4, 2023 19:16

@TedShifrin thanks! half my problem is i don't even know what to google for this, so much appreciated :)

Auden Young

Jul 4, 2023 19:15

@copper.hat also, i hope everyone's okay - very sorry this happened!

Auden Young

Jul 4, 2023 19:14

@s.harp hm, okay - i'll ask in the physics chat room then!

Auden Young

Jul 4, 2023 19:12

@Jakobian see that's what i was wondering, but this is in a math class' notes - admittedly one aimed at engineers, but still

Auden Young

Jul 4, 2023 19:10

dumb question of the day - what does it mean to 'find an integral' of a system of differential equations (the system is first order and hamiltonian, if that matters)? does it just mean to find a solution...?

Auden Young

Jun 22, 2023 04:24

it's easiest to see if you compare the area below say $\sqrt{x}$ to the area to the left of say $x^2$

Auden Young

Jun 22, 2023 04:23

So, it helps to sketch what you're doing here - if you're integrating between the x-axis and a function, you're finding the area between the x-axis and the function. If you're integrating between the y-axis and a function, you're finding that corresponding area. To get it into the format of the former, we want to reflect that area across the line $y=x$, which is exactly what finding the inverse of a function does

Auden Young

Jun 21, 2023 22:36

thank you very much!

Auden Young

Jun 21, 2023 22:34

Oh, I'm a moron

Auden Young

Jun 21, 2023 22:34

$(t-1)^2$

Auden Young

Jun 21, 2023 22:33

sorry, I'm not trying to be difficult - I understand the thing I'm getting using the table is wrong; it doesn't match Mathematica, as you confirmed. are you asking what formula I'm using in the table or something else? sorry

Auden Young

Jun 21, 2023 22:32

since I split it up by linearity and pull the constants outside, and then the table has $\mathcal{L}\{1\} = \frac{1}{s}$, and the second term seems to match what I described above