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It's 7, because if we look at the equation upside down (which is how you look at equations), you will see 01 + 6, which is equal to 1 + 6, and that is 7.  

@veryhasted @SilenceKiller99 @EonBen I have posted the solution. 8 hours to upload    

@GeorgeHudock you know he asked that over 2 years ago right? 

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On 26.4.2016 at 5:29 PM, Eirias said:

Since I'm sure y'all have no idea what the notation even means,  ψ  is the wave function. You need to look up at the chart and plug in the corresponding wave function. ψ* is the complex conjugate of that wave function.

571f87dc19d82_physicshwproblem.PNG.a1484

571f888f4772a_WavefunctionofHatom.PNG.08

Well thats an easy one:

L_z is the angular momentum operator in z direction based on a cartesian coordinate system

The equations on 1 and 2 are just a bra - vector multiple an operator multiple a ket - vector which you have to find by using the quantum numbers l,m and n to the correct spherical harmonic.

You even have the definition of those given so just throw the spherical harmonics into the integral and solve it, right?

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1 hour ago, Mirosius said:

Well thats an easy one:

L_z is the angular momentum operator in z direction based on a cartesian coordinate system

The equations on 1 and 2 are just a bra - vector multiple an operator multiple a ket - vector which you have to find by using the quantum numbers l,m and n to the correct spherical harmonic.

You even have the definition of those given so just throw the spherical harmonics into the integral and solve it, right?

Exactly. There's no physics knowledge needed because it's all in the problem . . . it's just a really, really nasty integral :)

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8 minutes ago, SilenceKiller99 said:

This is so obvious. Don't know why you won't get this in secondary school.

No kidding, still don't understand even a thing of it. Still don't understand what an integral is. I am probably just stupid. 

m=-1 isn't even in the Table. How would you solve the first problem?

I am working on the video as we speak :)

Trying to figure out a good camera angle though....

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4 hours ago, veryhasted said:

Still waiting on that video @Eirias :kappaross:

Oh yeah, sorry. I recorded it but the file corrupted, and then I moved twice and forgot about it. Let me see if I can't rig something up and record another one today (but it will be a couple days before upload, because of my terrible upload speed rn).

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On 28.4.2016 at 8:51 PM, EonBen said:

since idk what it is either, guess you better make it pretty basic XD 

The goal of an integral is to provide you the area enclosed by a function. y(x) for example.

You can approximate that area by adding the values of y(x) for x=m,m+1,...,n-1,n with the integral starting at x=1 and ending at x=n. In mathematical terms that means you draw rectangles with the width 1 and the height y(x) for every x. By adding them together you get the approximate area beneath the function y(x).

To get the exact area we need the steps on the x-axis to be way smaller. Infinitesimal small to be exact. By using infinitesimal small steps it is possible to get exact formulas to calculate the area beneath our function y(x). I'll spare you the formula as you can find it via google in a matter of seconds.
I could dive way further into the topic but I doubt anybody is interested in that. Whoever wants to study something that needs maths will encounter this sooner or later anyways.

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4 minutes ago, Kaliber84 said:

y(x) for x=m,m+1,...,n-1,n with the integral starting at x=1 and ending at x=n

You mean starting at x=m?

But yeah, Riemann sums are a good way to introduce the concept on integrals. However, since I'm going to be integrating irrational functions, I think I'm going to just call integration a type of operation that changes one function to another, and explain in terms of position, velocity, time.

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@Eirias Yeah. I wanted to do a general scenario not an explicit one.

Sure you can do what you said. But if you only give examples then the general meaning of an integral is lost don't you think? I'd use examples to explain what an integral is generally used for.

For example there is a function f(x,t) that describes the brightness at any place in a village at any time of day. The mayor wants to build a few solar panels and looks for the best place for them.
The best place would be where the sun shines the most intense over a day. By integrating the function over time we get a new function F(x,t) that shows the amount of light that has been accumulated at any place in the village for a time t. We could look to find a maximum here.
If the mayor wanted to build solar panels everywhere then we could integrate F(x,t) over the way to see how much light is accumulated in the whole village for a time t.
If we had started by integrating f(x,t) over the way we would have gotten a function describing how fast light is being accumulated in the whole village.

I think the easiest thing to logically connect integrations with their original functions is by knowing that a derivative of a function describes the gradient of the function. So a normal function describes the gradient of the integral of the function. Hope it was easy to understand.

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2 hours ago, Kaliber84 said:

@Eirias Yeah. I wanted to do a general scenario not an explicit one.

Sure you can do what you said. But if you only give examples then the general meaning of an integral is lost don't you think? I'd use examples to explain what an integral is generally used for.

For example there is a function f(x,t) that describes the brightness at any place in a village at any time of day. The mayor wants to build a few solar panels and looks for the best place for them.
The best place would be where the sun shines the most intense over a day. By integrating the function over time we get a new function F(x,t) that shows the amount of light that has been accumulated at any place in the village for a time t. We could look to find a maximum here.
If the mayor wanted to build solar panels everywhere then we could integrate F(x,t) over the way to see how much light is accumulated in the whole village for a time t.
If we had started by integrating f(x,t) over the way we would have gotten a function describing how fast light is being accumulated in the whole village.

I think the easiest thing to logically connect integrations with their original functions is by knowing that a derivative of a function describes the gradient of the function. So a normal function describes the gradient of the integral of the function. Hope it was easy to understand.

Well, obviously it was easy for ME to understand :). But to someone who doesn't know, I'm not sure. TBH though, I don't think anyone who hasn't completed calculus 2 will understand anything in the video, so I'd rather not bore those who can follow along.

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@Eirias True. In school I didn't even really care what the things were used for or why they were necessary. Only at uni did I really learn the logical foundation of the things. I think we had 2-4 weeks to do everything from high school again before we went on to the more advanced stuff in my first semester.

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13 minutes ago, Kaliber84 said:

@Eirias True. In school I didn't even really care what the things were used for or why they were necessary. Only at uni did I really learn the logical foundation of the things. I think we had 2-4 weeks to do everything from high school again before we went on to the more advanced stuff in my first semester.

I had a more advanced high school experience, so my whole first semester of college was basically review.

 

Also, finished recording the video, so just have to edit and post it.

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yeah, at first I followed it a bit, because it looks like the physics I had at secondary school. But then you started using that strange integral symbol thingy, and you lost me completely! xD

Edit: I followed the velocity and acceleration part at the beginning.

Edited by SilenceKiller99
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56 minutes ago, SilenceKiller99 said:

yeah, at first I followed it a bit, because it looks like the physics I had at secondary school. But then you started using that strange integral symbol thingy, and you lost me completely! xD

Edit: I followed the velocity and acceleration part at the beginning.

Yeah . . . that was a review of the foundations to understand the problem :)

1 hour ago, veryhasted said:

So after all the answear was just   - h  ? That's some complicated math for some a simple answear :o

You gotta love physics professors!

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