Brilliant. Well presented and explained. Only few people who can really clarify the physical concepts and hunt for the links relating to the physical situation.
Huge fan of your videos - the explanations are oftentimes much better than the ones provided by the professors at my University. For that reason I really hope that you might soon upload the video on Scattering, as this topic haven't really been covered to well in my class, and I would genuinely like to understand it ! :))
I am also looking forward to watching the lecture videos on Scattering. Hope you'll upload the video soon. BTW, I really like your videos. It really helps me to understand more quantum physics
In the video we explain that identical particles can be distinguishable or indistinguishable (the latter applied in quantum mechanics). I hope this helps!
Electrons are fundamentally identical and indistinguishable. Because they are fermions, no two electrons can occupy the same state, and the two electrons you are describing occupy different states, so in principle they are in a two-electron state that is possible. I hope this helps!
But what makes us so sure that identical classical particles can be distinguished? It seems obvious, but why? We can bounce photons off two electrons ( quantum) or two baseballs ( classical) .... but does the uncertainty principle prevent us from knowing which electrons are involved in the precise trajectories at the moment t of closest approach?
Not sure I entirely follow your argument. For baseballs, quantum mechanics is essentially irrelevant (e.g. de Broglie wavelength much smaller than relevant lengthscales). As such, you can always directly follow the trajectory of individual baseballs. I hope this helps!
By opposite spin I guess you are thinking about two electrons with opposite m_s quantum number (+1/2 and -1/2). We actually go over a similar case in this video: ruclips.net/video/-HMZNk6VlZ0/видео.html Overall, I would recommend following the full playlist on identical particles to appreciate all the subtleties: ruclips.net/p/PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf I hope this helps!
Not always. If they are in an entangled state they can always be opposite, but also be indistinguishable. Quantum mechanics has a lot of weirdness to it.
I've read some definitions of the Pauli principle saying "two indistinguishable particles can not occupy the same antisymmetric state", but this would not include systems of Fermionic atoms? Say a system of Li6 and He3, these would not be indistinguishable right? How does this work out? Is there a definition of the Pauli principle including all possible cases?
Yes, Li6 is indistinguishable from He3. This means that the overall state of this system need not be totally symmetric or totally antisymmetric. The Pauli principle is not a definition, it is a consequence of the symmetrization postulate when applied to fermionic indistinguishable particles, which states that the overall state must be totally antisymmetric under particle exchange. We go into some detail about how all of this works in our playlist on identical particles: ruclips.net/p/PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf I hope this helps!
No expert in quantum cryptography, but I think that what is needed is to exploit the properties of entangled states, which can naturally be captured by two particles. I would however recommend you read more about this elsewhere! :)
Communication can be done with or without entanglement. The famous BB84 protocol uses just superposition and the fact that polarization has only two orthogonal states to communicate without entanglement. Another one that uses superposition is counter factual communication which is very “spooky” in the way it works. There are methods that use entanglement as well, one example being the use of a Franson interferometer (although that is used more to detect eavesdroppers rather than communicate directly.
Is it correct to say that qm identical particles are indistinguishible unless they don't interact? For instance if we have two identical particles, with their own spin state psi-1 and psi-2 and they don't interact, they are (IMO) distinguishible; is this right? - thank you for any answer.
Even if they don't interact, they are actually indistinguishable. If you consider two free non-interacting particles in the position representation with their wave functions overlapping, then you still cannot distinguish them. A more fundamental reason comes from the symmetrization postulate etc. that we discuss in the subsequent videos in this series. I hope this helps!
@@ProfessorMdoesScience thank you very much for your tremendously quick answer! I understand that two identical particles might have overlapping wave functions in the position representation even without interaction (due to their previous history, I guess). So can we consider two qm particles distinguishible if their wave functions don't overlap, or if their overlap is 'minimal' in some sense? Thank you again!
@@paolofazzini3146 If there was no overlap (e.g. they are very far away from each other), you could in principle treat them as distinguishable to start with. But in any relevant quantum system, they will eventually overlap, and therefore the best approach is to directly treat them as indistinguishable. I hope this helps!
@@ProfessorMdoesScience that is very enlighting, thank you again. The reason of my doubts is that I've found the combined state vector of two spin-equipped particles (say protons) as psi=a*|up-up>+b*|up-down> +c*|down-up>+d*|down-down> (an instance of the tensor product of their respective spin spaces) This expression comes with the caveat that this form for the state vector applies if they are "distinguishible" (in some textbooks or papers) or "noninteracting" (in some other docs). So for indistinguishible particles the above expression is incorrect? I apologize for the proliferation of my questions; I promise this will be the last one for a while :-)
@@paolofazzini3146 Without the full details of your sources, my guess is that they are referring to the fact that for indistinguishable fermions (e.g. protons), the wave function must be totally antisymmetric, which places constraints into the values that the coefficients a, b, c, d can take. If you follow our series on identical particles, you will find a full discussion of these ideas: ruclips.net/p/PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf I hope this helps!
Brilliant. Well presented and explained. Only few people who can really clarify the physical concepts and hunt for the links relating to the physical situation.
Thanks, I'm glad you liked it!
Huge fan of your videos - the explanations are oftentimes much better than the ones provided by the professors at my University. For that reason I really hope that you might soon upload the video on Scattering, as this topic haven't really been covered to well in my class, and I would genuinely like to understand it ! :))
Glad to hear, and we hope to publish the scattering videos soon! May we ask where you study?
I am also looking forward to watching the lecture videos on Scattering. Hope you'll upload the video soon. BTW, I really like your videos. It really helps me to understand more quantum physics
where is the scattering background? Hope it coming soon
We'll try to get to it as soon as possible! :)
Thanks, very clear! If you have time, it would be excellent if you could also post the Scattering lecture.
Thanks for the suggestion, it is definitely on our to-do list!
awesome..my masters course has the same topic now ..and i got it from you
Great timing! If you find our videos helpful, share them with your friends, it helps us grow! :)
Very well explained 👍thank-you so much
Glad you like it!
Really helpful, thank you for making this!
Thanks for watching, and glad you like it!
Nice video. But why does everyone call this situation "Identical Particles" when they should call it " Indistinguishable Particles"?
In the video we explain that identical particles can be distinguishable or indistinguishable (the latter applied in quantum mechanics). I hope this helps!
Super helpful, thank you very much!!
Glad you find it helpful!
If two electrons in a atom having different spin and mommentum but still having a overlapping wavefunction ,can they be indistinguished or not ??
Electrons are fundamentally identical and indistinguishable. Because they are fermions, no two electrons can occupy the same state, and the two electrons you are describing occupy different states, so in principle they are in a two-electron state that is possible. I hope this helps!
But what makes us so sure that identical classical particles can be distinguished? It seems obvious, but why? We can bounce photons off two electrons ( quantum) or two baseballs ( classical) .... but does the uncertainty principle prevent us from knowing which electrons are involved in the precise trajectories at the moment t of closest approach?
Not sure I entirely follow your argument. For baseballs, quantum mechanics is essentially irrelevant (e.g. de Broglie wavelength much smaller than relevant lengthscales). As such, you can always directly follow the trajectory of individual baseballs. I hope this helps!
If the two particles have opposite spins,then can we tell which particle is which?
By opposite spin I guess you are thinking about two electrons with opposite m_s quantum number (+1/2 and -1/2). We actually go over a similar case in this video: ruclips.net/video/-HMZNk6VlZ0/видео.html
Overall, I would recommend following the full playlist on identical particles to appreciate all the subtleties: ruclips.net/p/PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf
I hope this helps!
@@ProfessorMdoesScience thank you very much..I will surely watch the video🤗
Not always. If they are in an entangled state they can always be opposite, but also be indistinguishable. Quantum mechanics has a lot of weirdness to it.
Great video, thanks a lot :)
Glad you liked it! :)
Well said sir ✌️
I've read some definitions of the Pauli principle saying "two indistinguishable particles can not occupy the same antisymmetric state", but this would not include systems of Fermionic atoms? Say a system of Li6 and He3, these would not be indistinguishable right? How does this work out? Is there a definition of the Pauli principle including all possible cases?
Yes, Li6 is indistinguishable from He3. This means that the overall state of this system need not be totally symmetric or totally antisymmetric.
The Pauli principle is not a definition, it is a consequence of the symmetrization postulate when applied to fermionic indistinguishable particles, which states that the overall state must be totally antisymmetric under particle exchange. We go into some detail about how all of this works in our playlist on identical particles:
ruclips.net/p/PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf
I hope this helps!
@@ProfessorMdoesScience Thank you so much! I will go through the playlist!
Sir can you tell me what is the benefit of using two particles quantum state instead of single particle quantum state in quantum cryptography
No expert in quantum cryptography, but I think that what is needed is to exploit the properties of entangled states, which can naturally be captured by two particles. I would however recommend you read more about this elsewhere! :)
Communication can be done with or without entanglement. The famous BB84 protocol uses just superposition and the fact that polarization has only two orthogonal states to communicate without entanglement. Another one that uses superposition is counter factual communication which is very “spooky” in the way it works. There are methods that use entanglement as well, one example being the use of a Franson interferometer (although that is used more to detect eavesdroppers rather than communicate directly.
Is it correct to say that qm identical particles are indistinguishible unless they don't interact? For instance if we have two identical particles, with their own spin state psi-1 and psi-2 and they don't interact, they are (IMO) distinguishible; is this right? - thank you for any answer.
Even if they don't interact, they are actually indistinguishable. If you consider two free non-interacting particles in the position representation with their wave functions overlapping, then you still cannot distinguish them. A more fundamental reason comes from the symmetrization postulate etc. that we discuss in the subsequent videos in this series. I hope this helps!
@@ProfessorMdoesScience thank you very much for your tremendously quick answer! I understand that two identical particles might have overlapping wave functions in the position representation even without interaction (due to their previous history, I guess). So can we consider two qm particles distinguishible if their wave functions don't overlap, or if their overlap is 'minimal' in some sense? Thank you again!
@@paolofazzini3146 If there was no overlap (e.g. they are very far away from each other), you could in principle treat them as distinguishable to start with. But in any relevant quantum system, they will eventually overlap, and therefore the best approach is to directly treat them as indistinguishable. I hope this helps!
@@ProfessorMdoesScience that is very enlighting, thank you again. The reason of my doubts is that I've found the combined state vector of two spin-equipped particles (say protons) as
psi=a*|up-up>+b*|up-down>
+c*|down-up>+d*|down-down> (an instance of the tensor product of their respective spin spaces)
This expression comes with the caveat that this form for the state vector applies if they are "distinguishible" (in some textbooks or papers) or "noninteracting" (in some other docs). So for indistinguishible particles the above expression is incorrect?
I apologize for the proliferation of my questions; I promise this will be the last one for a while :-)
@@paolofazzini3146 Without the full details of your sources, my guess is that they are referring to the fact that for indistinguishable fermions (e.g. protons), the wave function must be totally antisymmetric, which places constraints into the values that the coefficients a, b, c, d can take. If you follow our series on identical particles, you will find a full discussion of these ideas:
ruclips.net/p/PL8W2boV7eVfnJ6X1ifa_JuOZ-Nq1BjaWf
I hope this helps!
At time 6:20 you mention the video about scattering. where is it ?
Unfortunately it is still in our (long) to-do list; we'll let you know when it becomes available.
Please keep going ....
good
oh so it's a property of waves and not QM
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Unfotunately I don't understand greek, and I think Google Translate is not quite giving me the correct translation...