ModCon

They simply disappear the next time I come back.

Why do my chat rooms not show up in ‘mine’ tab under rooms?? 🤨

I will be grateful if someone can help me with my question. Doubts about analytical mechanics have been eating my head for a few days now :/

I am not able to understand a seemingly simple thing. Why does constraints being scleronomous imply position does not explicitly depend on time?

@StanShunpike one of the protaganists of big bang theory (tv show)

The one on which you left a comment

@ACuriousMind Hey, sorry for following you all the way till here but can you please help me out with my question?

Oh okay.

Aaaah okay :(. Would you be able to help me with some other questions related to analytical mechanics or is it an area you haven't studied at all?

@JohnRennie Could you please help me with this question? I am not able to understand a seemingly simple thing. Why does constraints being scleronomous imply position does not explicitly depend on time?

Okay.

@DavidZ Could you please name some/one of them where I may ask my questions? Thank you.

Oh okay.

@DavidZ Sir, may I ask you for an explanation to my question?

Okay I will do that.

Can someone please help? I will be very grateful. This and other doubts in analytical mechanics are eating my head :(

I am not able to understand a seemingly simple thing. Why does constraints being scleronomous imply position does not explicitly depend on time?

Oh ok :((. Thanks for your time.

let me ask you the main doubt: my textbook shifts from saying T(q, \dot q, t) to T(q, \dot q) without mentioning anything. Why is it okay to do this?

But then say I have my kinetic energy T=T(q, \dot q, t) vs T(q, \dot q), in both cases the expression for variation of T (𝛿T) will be different since one will have partial derivative with respect to time and other one wont

and then some people like the post I mentioned in my comment in the SE post talk about there being a need for explicit dependence or something like that

What confuses me is that things are written to be functions of q and t where they aren't explicitly there in the expression

but is there a consensus on whether explicit dependence on a variable is needed or not to call it a function of that variable like generalised coordinate?

Yes this.

The question about how to see kinetic energy is a function of q, \dot q and t

May I ask you a couple of doubts related to the question of mine on which you left a comment?

Yes. I am incredibly sorry for pestering you like this.

Ok. Thanks a lot for your time. Cleared quite a few things today.

Hehe I get that. However I have seen questions which ask where for orbitals like 2p or 4p. So here it evaluating over points or spheres wouldn't make a lot of sense. What is expected here?

But wouldn't the psi change in coordinate system to system?

Yep that's ok

I am quite a bit confused about this.

Ok so if someone asks where is the probability of finding electron maximum in a particular orbital, what does it mean? What do we maximise (like Ψ^2*dV)?

I meant (absolute value of Ψ)^2

What exactly is Ψ^2*dV used for? Now I know it isn't for comparing probabilities at different points, is it for finding regions of maximum probability for 2p, 3d and such non spherical orbitals?

Hey Ivan, now I understand that I messed up with different probabilities

I do agree with you. But to answer where is the probability of finding maximum, simply evaluating probability density wouldn't do the job. For 1s we may evaluate probability of finding between r and r+dr using volume of shell to get the answer. But say we have to do it for 2p. Then in this case, we cannot directly use density to compare, since even in 1s, using simply density gives points at nucleus as points of maximum probability, but there isn't any volume there (volume of shell becomes zero at nucleus), meaning there aren't any points there too. How should I do this for 2p orbital?

But we can use simply probability density to compare points only when all of them have same dV, which they don't have. Otherwise I get the point.

We have probability density right there, but since we are interested in actual probability at a point (i.e. around it) and not just probability density, shouldn't we multiply density by volume to get the actual probability?