6:53 to 7:05 Explain__ Since we have complex # and it is hard to see bump on complex value function; we will take norm of that function. But this does not seem logic of taking norm.
Taking the norm will give you the magnitude of the complex number/wave as a real value - it is easier to show how the peak position depends on k_0 when we don't have to think about the phase of the complex number.
What he meant was this. You have phi(x,0) , in it change x--> x-(dw/dk)t , so you get an equation of phi(x-(dw/dk)t , 0) . Then see that in the final expression of phi(x,t) the integral is nothing but phi(x-(dw/dk)t , 0). So the final equation becomes phi(x,t) = exp[-iw(k_not)*t + i*(dw/dk)*t ]*phi(x-(dw/dk)t , 0) . Just take the mod both side and your get the equation your saw. replace the integral part
Rodolfo Jr. DelRosario you see,acc. to De-broglie,every classical particle,or any object can be treated as a localised wave. A wave packet is a possibility in space of having found a particle at a particular location. This helps us understand how particles can be related to waves. Plus,we can think of a photon as a localised wave(wave packet) in space,thus ascribing a position to it,but causing a huge uncertainty in d momentum.
Pure , plain wave ca'nt transmit information. Think about this, a simple note on the piano means nothing, but if you transmit a musical phrase, you have music. On the other hand, if you scream you can´t give others information, but a group of sonuds (words), can give others a lot of. In the same way, when you have a group of simple monotonic waves and put them into a packet, you can trasmit information. The packet moves with group velocity.,
Nothing. It's just easy to calculate, but in general nature doesn't care about them much. That's not how the real theory works. He simply can't show you how the real theory works, it's mathematically too hard.
Becuase its the exponantial function evaluated at the remainder of the taylor series, which at values close to k_0 can be set equal to 0. exp(0) = 1, hence it can be ignored.
I thought it necessary to post this here in light of circumstances and things factual. Aside from the fact my PhD from this institution was stolen by DoD, there seems to be some confusion. You see, after watching lectures like this for months on end, people in counter terrorism have no idea if this is real or not. So if a foreign advesary got a hold of this, they make sure that advesary has Access to me doing as I do based in part on this. Yet they claim to have no idea if things like this as illustrated are real or made up? 🤔 I find that particularly problematic as circa 2015, I be live the media stated the Pentagon funded this fine institution 5 billion or so per annum? So not knowing if things like this are real, let's just throw 5 billion away and meanwhile force me to rot over a degree stolen on illegal order by HR McMaster, and my stolen money for solving a certain math problem, and let's look past perjury and obstruction as to help someone acquire fissile material for profit at my expense. Yet ladies and gentleman, these same people are oblivious as to what's legit and not in nuclear physics and fields like it, but don't say anything as it's all classified! So I guess TH-cam is a classified resource too along with MIT-but they don't know if that's fake or not, and purposely not hire me on account of a degree I was screwed out of twice, yet I'm the go to man to prosecute people by force and for free as...they went to college. So we know that qualifies them! So the guy with the stolen PhD watches things like this and writes notes from it; is it real? 🤔 College education and 5 billion per annum and DoD can't figure this out. Thank you MIT for my PhD circa 2019? It's almost 2023 and I've yet to see it. 😐 makes me wonder if that's in fact real or not. 🤔
@@jelmar35 Its called I actually qualified in 2 fields, and then a 2nd institution in the UK awarded me a 3rd PhD. Someone crooked in leadership in conjunction with a crooked Sr DOJ official decided to tell some tall tales about me being a threat to national security to get a warrant to seize all 3 of my PhD's on spite. The irony? They were running a corrupt enterprise, and funding terrorism accordingly. Self explanatory.
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Here comes calculus gathering the infinitesimal small parts.
Thanks ❤️🤍
admito que me he perdido
Yo me duermo de vez en cuando. Lo que hago es lo dejo, y vuelvo más en El día. Y veo un vídeo 2 o 3 veces.
sir, you have given presentations of very important results about wave packets...Can you help me to check it out...
This is helpful ❤️🤍
6:53 to 7:05 Explain__ Since we have complex # and it is hard to see bump on complex value function; we will take norm of that function. But this does not seem logic of taking norm.
Taking the norm will give you the magnitude of the complex number/wave as a real value - it is easier to show how the peak position depends on k_0 when we don't have to think about the phase of the complex number.
What he meant was this.
You have phi(x,0) ,
in it change x--> x-(dw/dk)t ,
so you get an equation of
phi(x-(dw/dk)t , 0) .
Then see that in the final expression of phi(x,t) the integral is nothing but
phi(x-(dw/dk)t , 0).
So the final equation becomes
phi(x,t) = exp[-iw(k_not)*t + i*(dw/dk)*t ]*phi(x-(dw/dk)t , 0) .
Just take the mod both side and your get the equation your saw.
replace the integral part
what is the importance of wave packets in classical and quantum mechanics?
Rodolfo Jr. DelRosario you see,acc. to De-broglie,every classical particle,or any object can be treated as a localised wave. A wave packet is a possibility in space of having found a particle at a particular location. This helps us understand how particles can be related to waves. Plus,we can think of a photon as a localised wave(wave packet) in space,thus ascribing a position to it,but causing a huge uncertainty in d momentum.
Pure , plain wave ca'nt transmit information. Think about this, a simple note on the piano means nothing, but if you transmit a musical phrase, you have music. On the other hand, if you scream you can´t give others information, but a group of sonuds (words), can give others a lot of. In the same way, when you have a group of simple monotonic waves and put them into a packet, you can trasmit information. The packet moves with group velocity.,
Nothing. It's just easy to calculate, but in general nature doesn't care about them much. That's not how the real theory works. He simply can't show you how the real theory works, it's mathematically too hard.
Can somebody explain in the 5:00 minutes time duration of lecture,,why the big exponential term rejected from calculation?
Becuase its the exponantial function evaluated at the remainder of the taylor series, which at values close to k_0 can be set equal to 0. exp(0) = 1, hence it can be ignored.
@@charlie2720 maybe no , that's the assumption
@@tibber4477 This is approximation already. It's a Taylor series
Best
The last example he gave is wrong !!
Which one 🤔
I thought it necessary to post this here in light of circumstances and things factual. Aside from the fact my PhD from this institution was stolen by DoD, there seems to be some confusion.
You see, after watching lectures like this for months on end, people in counter terrorism have no idea if this is real or not. So if a foreign advesary got a hold of this, they make sure that advesary has Access to me doing as I do based in part on this. Yet they claim to have no idea if things like this as illustrated are real or made up? 🤔
I find that particularly problematic as circa 2015, I be live the media stated the Pentagon funded this fine institution 5 billion or so per annum? So not knowing if things like this are real, let's just throw 5 billion away and meanwhile force me to rot over a degree stolen on illegal order by HR McMaster, and my stolen money for solving a certain math problem, and let's look past perjury and obstruction as to help someone acquire fissile material for profit at my expense.
Yet ladies and gentleman, these same people are oblivious as to what's legit and not in nuclear physics and fields like it, but don't say anything as it's all classified! So I guess TH-cam is a classified resource too along with MIT-but they don't know if that's fake or not, and purposely not hire me on account of a degree I was screwed out of twice, yet I'm the go to man to prosecute people by force and for free as...they went to college. So we know that qualifies them! So the guy with the stolen PhD watches things like this and writes notes from it; is it real? 🤔
College education and 5 billion per annum and DoD can't figure this out. Thank you MIT for my PhD circa 2019? It's almost 2023 and I've yet to see it. 😐 makes me wonder if that's in fact real or not. 🤔
What?
@@jelmar35 Its called I actually qualified in 2 fields, and then a 2nd institution in the UK awarded me a 3rd PhD. Someone crooked in leadership in conjunction with a crooked Sr DOJ official decided to tell some tall tales about me being a threat to national security to get a warrant to seize all 3 of my PhD's on spite. The irony? They were running a corrupt enterprise, and funding terrorism accordingly.
Self explanatory.