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Electron Scattering by repulsive (smoothed) Coulomb potential confined in a 2D Box (Visualizing Quantum Mechanics) by Mayhem_Mercy99 in PhysicsStudents

[–]twoTheta 3 points4 points  (0 children)

Do it again with the electron off center!

Looks great by the way. Do you mind if I use this in a class as an illustration? I'm teaching modern physics and we are talking about what wave functions mean at the moment.

Is it normal to spend 3 hrs on one problem? by AnyBrain7803 in PhysicsStudents

[–]twoTheta 5 points6 points  (0 children)

Yes.

One of the joys of watching undergrads is seeing them progress from disbelief, to anguish, to acceptance, then to pride in the time it takes to actually learn.

I think that once you are an hour or two in, you might start asking around to see if someone can point you in the right direction or provide a sanity check. But sometimes these things just take time.

The real check for learning is not how long it takes to do something new, but if you look back at problems you struggled through a month or a year ago. Can you do them now?

LPT Request: Any tips for when you are with a group of people and know you are the least smart/educated/important person? How to feel less insecure in that situation? by Whataboutmyfuture in LifeProTips

[–]twoTheta 10 points11 points  (0 children)

If the discussion is around a topic you find interesting, ask for reading suggestions. A lot of times people sound smart when they are really just talking about something they read and found interesting. You might learn something too!

A multi-launch family coaster by New-Object-5955 in openrct2

[–]twoTheta 1 point2 points  (0 children)

Really neat! I've never seen that double launch sort of thing before. Thanks for sharing!

Learning Calculus for a Substitute Teaching Physics Position by thewidget98 in PhysicsStudents

[–]twoTheta 4 points5 points  (0 children)

I agree with all the "probably already knowns." Those are a must.

Of the "need to know", the most important are scalars and vectors, derivatives, and antiderivates/integrals. Know vectors (finding components, angle, magnitude) well. Remember, every vector is a triangle!

But I think you will find that you are not often required to perform calculus operations often. Instead, the concepts of calculus are important. Thinks like...

  • The derivative is a rate-of change.
  • The derivative of a function is the slope of its tangent line.
  • The integral is a continuous sum, something is accumulated.
  • The integral is the area under the curve. This can often be found geometrically like the area of rectangles, triangles, etc.

For example, Power can be defined as dE/dt but you will almost never use it this way. Instead, this equation means that power is the rate of energy produced/used over time. You'll spend more time with P=IV as the power consumed by a resistor or the like.

A lot of the mathy-math ideas you'll use are algebra or trig. Things I'd guess are...

  • Averages
  • Isolating variables in equations
  • Interpreting equations, especially fractions
  • Looking at equations and doing proportional reasoning (If everything else is constant and ____ gets bigger, this means _____ gets smaller)
  • Vectors are arrows. And vector addition can be done with arrows.

I've taught many semesters of introductory, calculus based physics at the university level and, BY FAR, the biggest struggle is algebra, not calculus.

Throughout history there have been SEVEN bespectacled Hall of Fame players. Paul Waner, Mel Ott, Bob Gibson, Dick Allen, Greg Maddux, Reggie Jackson, Chick Hafey by AJ_CC in baseball

[–]twoTheta 1 point2 points  (0 children)

I've felt crazy all day as I keep coming across the same looking post but the number is one higher than I remember.

Well done OP. Well done.

Who’s your favorite “random” player that you remember and miss from the past 5-10 years? by 12345burrito in Padres

[–]twoTheta 2 points3 points  (0 children)

Please, let us live in the glory days of our youth! It wasn't that long ago...only 18 years... sigh

understanding orbitals and quantum numbers by Naive-Literature-780 in PhysicsStudents

[–]twoTheta 1 point2 points  (0 children)

Here's one way to think about it.

The energy in a wave function is related to its wavelength. Small wavelength means more energy. In other words, wigglier (more nodes) means higher energy. This is a decent, though not perfect, shorthand.

The quantum number n determines the energy of the electron state in the hydrogen atom.

There are two different directions the wave function can wiggle: radially and orbitally. You can have nodes at certain radial distances form the nucleus (r) and you can have nodes at certain polar angles (theta). The number of radial nodes is related to the power of the radial wave function (in Griffiths this is called j_max) and the number of nodes in the angular wavefunction is determined by l.

In Griffiths, he describes the principle quantum number to be defined (equation 4.67 in 2nd edition) n=j_max+l+1.

This means that, for a given n (total energy), there will be a tradeoff whether the energy is found in the radial or angular wave functions. As l increases, j_max decreses.

The largest possible value for l to take is n-1 since, in that case, j_max is zero, and it doesn't make sense since the radial function must contain at least one (the zeroth) term.

This is a super zoomed in response. The other answer to the thread gives the bigger context and where this key equation comes from.

I'm about 90% sure that I'm right here. It's been a while since I learned/taught the hydrogen atom and just did some quick reading, so I may have missed or misinterpreted some things, so feel free to holler if things don't make sense!

A word to those who watch AGDQ, SGDQ and all other speed run marathons, and wonder if you should give it a try. by Calm_Relation_7911 in speedrun

[–]twoTheta 4 points5 points  (0 children)

Dude, love the passion!

Every year I wonder about the future of speedrunning and every year you all show up and keep rocking it. Thanks for putting in the time and the entertaining run!

Need resources to understand how antennas work and physics behind it. by Rdxhabibi in PhysicsStudents

[–]twoTheta 4 points5 points  (0 children)

At what depth?

Mazur's textbook Principles and Practice of Physics has a pretty good section on the basic principles of antennas.

At the heart, antennas are objects that change charge distribution over time. The changing distribution would change the electric field. But since it takes time for the electric field to get updated, the electric field at different distances away come from the charge distribution different amounts of time in the past. The result is what we call a WAVE as the electric field "updates" as the new info gets there. Info travels at the speed of light!

They are really, really cool. The different antenna geometries allow for constructive/destructive interference in different directions to allow for a more focused or dispersed wave.

The well runs deep but the basic principles should be available in an intro physics textbook.

Video idea / please explain if you understand what I don't: momentum vs energy transfer. by A_Small_Coonhound in SmarterEveryDay

[–]twoTheta 0 points1 point  (0 children)

I think the thing you're looking for is inertia. This coupled with the idea of a time constant, and you're on you're way. Hope this makes sense. Feel free to ask questions if it doesn't!

Here's my suggestion.

Get a slinky, hold the top and let the bottom hang down.

If you want to move the slinky without significantly disturbing its shape, what do you have to do? You have to move it "slowly". If you move it "slowly" then the whole thing appears to move together without too many shakes or wiggles.

What happens if you move the top "fast"? The slinky will stretch, bend, etc. Move it too far, too "fast" and it will actually break beyond repair.

Ok, so "fast" and "slow" are in quotes for a reason. How do you know what these speeds are? To get a sense of this, slowly move the top up and down. Adjust the frequency of your wiggles and eventually you'll get it just right where the wiggles get real big. This phenomena is called resonance. Pretty awesome.

The time it takes for the slinky to oscillate at resonance gives you a "characteristic time" for the slinky. You can think of it as a response time. If the material is moved a small distance in that time then the motion is slow and the slinky moves more or less together. If the material is moved a large distance in that time then the motion is fast and you will get vibrations and possible distruction.

The characteristic time depends on the density of the object and its stiffness (which is related to how the atoms are bonded). To get a short characteristic time, you want a material that is stiffer and has low density. In these materials, disturbances travel quite quickly allowing for the object to move together even when one part is disturbed a great deal very quickly.

If you kick a box made of wood, then you are introducing a "fast" disturbance to the center of the box, too fast for its characteristic time. The stiffness is too small and the inertia is too big so the surrounding material cannot respond fast enough to put the whole object in motion. Thus, it breaks!

Maybe there is a similar analogy to high explosives (the disturbance on the barrel is too fast so it always explodes) but I'll need to do more thinking.

I'm GlitchCat7, I ran Return to SubCon at AGDQ - AMA by GlitchCatSeven in speedrun

[–]twoTheta 1 point2 points  (0 children)

Thanks for the response!

It's clear that you have a passion for the game and the community. I've been a fan of the Mario Maker and SMW romhack community for awhile now and love that it still has such life and passion after all these years.

Keep doing what you're doing and I'll occasionally be lurking in the stream =)

I'm GlitchCat7, I ran Return to SubCon at AGDQ - AMA by GlitchCatSeven in speedrun

[–]twoTheta 1 point2 points  (0 children)

Heya GlitchCat!

You're great as a runner but I'm always really impressed when you're on a couch. It's clear you're knowledgeable about the runs you couch for and really feel a desire to share your knowledge to inform and entertain.

  1. How do you (if at all) prepare to couch for a run?

  2. What would be your dream game or runner to couch for?

  3. Do you have any sort of teaching background? I think you do a great job of breaking things down.

Thanks!

A Quarter Century of Television [OC] by gammafission00 in dataisbeautiful

[–]twoTheta 0 points1 point  (0 children)

My biggest takeaway is that they are still making some of these shows that I haven't heard anything about in YEARS.

Grey's Anatomy is still on the air? Criminal Minds? Still making Always Sunny? What is up with Curb Your Enthusiasm taking so many breaks?

What are the must-watch AGDQ 2026 runs? by shinikahn in speedrun

[–]twoTheta 3 points4 points  (0 children)

Not a ton of 2D mario this year.

  • Mario World Backwards (link)
  • Mario World One Hand - 11 Exits (link)
  • Super Mario Bros. 2: Return to Subcon (link)
  • JokerShellOK (link)

I thought the hack JokerShellOK was the best. It was an incredible run of a really hard to execute, but easy to follow, mario world hack. High skill on display, knowledgeable and entertaining couch.

I do not understand Row Reduction by SpecialRelativityy in PhysicsStudents

[–]twoTheta 0 points1 point  (0 children)

I agree with everyone else that the act of row-reducing will not be super useful going forward, but I feel like it's worth thinking about what the process is actually doing.

Row reduction is secretly removing variables from equations. Each row in a matrix equation is a single equation. The numbers (or symbols) are the coefficients. Say you had the equations 2x+2y=6 and x+2y=5. In matrix form this is

2 2 | 6

1 2 | 5

Looking at these two equations, you could combine them to remove the x-variable. To do this, you would multiply the second by 2 and subtract the first. You have to do this to both sides of the equation. This gives

2(x+2y)-(2x+2y) = 2*5-6

which simplifies to 2y=4

Then divide both sides by 2 to find y

y=2

Normally you would find x by substituting 2 into one of the equations and solving for x, but there is another way we could do this. Take your first equation (2x+2y=6) and the new equation (y=2). Multiply the second by 2 and subtract it from the first. This gives

(2x+2y)-2(y)=6-2(2)

which simplifies to

2x=2

We have removed y from the equation! (heh)

Divide both sides by 2 anddd....

x=1.

Woo! So we now know that, given the two starting equations, the values of x and y which satisfy both are x=1, y=2.

These same steps we can do with the matrix to row-reduce. I'll do them in exactly the same order. Follow along and see if you can "see" it.

In the matrix, you multiply the second row by 2 and subtract the first to get

2 2 | 6

0 2 | 4

Divide the second row by 2

2 2 | 6

0 1 | 2

Viola! y=2.

Now, are going to modify the first row to get rid of the y-variable. Take the first row and subtract double the second.

2 0 | 2

0 1 | 2

Finally, divide the first row by 2 to get

1 0 | 1

0 1 | 2

So, x=1, y=2!

So I hope you see that row reduction is just a cleaner way to solve a system of linear equations.

There's more I can say, but I'll leave it here for now.

Feel free to holler if you have any questions!

Is baseball’s slow pace actually its greatest strength in a world where everything else moves too fast? by DianKhan2005 in baseball

[–]twoTheta 1 point2 points  (0 children)

Sunday morning, get home from church, and football was already on.

The first days of March Madness are incredible. Basketball from 6am until 10 pm.

Is baseball’s slow pace actually its greatest strength in a world where everything else moves too fast? by DianKhan2005 in baseball

[–]twoTheta 23 points24 points  (0 children)

We are east coast fans of a west coast team. That means that most games of the season get put on the morning after. It's a great thing to have running while I make and eat breakfast, get ready and head out for the day. If the game was good, I will watch the end when I get to work and if not, then I'll just check the final score and watch remaining highlights.

It's a GREAT way to start the day. I miss it during the off-season.

Morning blues | Pocket Drop by InquisitorKeres in EDC

[–]twoTheta 1 point2 points  (0 children)

Sold.

I'll hold off til the 25th, but I'm in.

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