I'd start with a short discussion of what it means to "simplify" in this context... student needs a little background here, but not a lot. ie. we want no nesting square-roots if we can help it.
In this working I am illustrating how I'd approach explaining how to approach these sorts of problems...
ie. if the e-p pair had aligned spins, then the probability of 2-photon annihilation is zero?
Is there a paper to back this up?
I am thinking of thought experiment where the spins of both particles are deliberately polarized.
They could have prepared initial polarization angles to whatever...
Pretty much in a nutshell... fielded a question about how spin affects electron positron annihilation... ie do the spins have to be opposite in order to conserve angular momentum for two-photon annihilation to happen?
Intuitively I figured that looks reasonable ... but decided to check, and...
OK well done.
The takeaway lesson here is to write it out... don't make people guess what you did.
The correct answer is not as important as how you got there ... and even an incorrect answer can be useful if we have that working and reasoning.
That's three questions. I trained as an experimentalist, let's see if I understand the questions ... taken in order:
Is (2) the only important equation for the experimentalist?
No ... depends on what we are testing. However, in the usual teaching lab experiment, we are mainly interested in the...
The suggested path is to treat the situation as if you had a full current in the entire big conductor without the cavities, and then add in the effect of having an additional current going the other way where the cavities should be.
Did you try that?
IRL the current would be on the outer...
Well let's see:
## \left[i\hbar\partial_t - H\right]\Psi = 0## $$ \left[i\hbar\partial_t - H\right]\Psi = 0$$
... comes out as: ## \left[i\hbar\partial_t - H\right]\Psi = 0## $$ \left[i\hbar\partial_t - H\right]\Psi = 0$$
... looks OK in preview, now to post so you can see:
Note: if you make a...
"The math seems to checkout but I'm unsure."
Well you got, "So she was 36 72 years ago and is 96 now." ... so let's check that: $$36 + 72 \neq 96$$
If she is 96 now, how old is she 72 years ago?
Nice try tho ... you got tripped up, I suspect, by trying to say too many things at once and not...
Stephen Tashi wrote:
"The word "hypothesis" can have different meanings."
... to be clear,I am deducing from context that "hypoithesis"in OP refers to "hypothesis testing" in applied math, specifically as taught at the senior secondary or starting tertiary level. Could be wrong.
I guess, still...
What Tom said... also the John Hopkins article cited is out of date using poor studies.
There are also BMJ papers about acupuncture as a complimentary treatment, and UK NHS used to fund it. BMJ is a mainstream peer reviewed journal. This is a low bar. BMJ papers can be wrongnir misleading, so...
Hypothesis testing is one way to verify the truth of the presuppositions in a syllogism.
Remember the conclusion is only true if the presups are true and the logic is valid.
So all deductive reasoning use hypotheses, and produces one.
It's how you choose what to test next.
ie. Say we have...
Since there is no verifiable medical effect beyond placebo, therefore there is no need to look further for a mechanism.
An acupuncture session could have va positive effect on your migranes.
What the session does is distract you from the migraine while you have a quiet lie down in a darkened...
Helps to think about how the physics described by the equations works.
Can you sketch the field?
Taking the x-axis pointing in the direction of the current before the bend ... what happens is the current changes direction to an angle to the x axis.
So did you have a think about some easy...
I'm in NZ. So you are 12-13? You are doing well then.
The worked examples in the link I gave you will be a bit offhand in showing reasoning because the author is writing for a college level audience.
Your High School's physics textbook (or of a High School near you) will probably be the best...
... so, in other words, "how would a stationary state change?" ... with the answer being, it does not: the physical state in real life is not absolutely the stationary one because the calculation left out some stuff.
Only going into detail.
Have I got it?
It's neat. Could it be an insights...