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Man, at the end of the video my mind was blowing, thanks a lot for making me understand these things! Grettings from Brasil, I am a master studente in QFT e yours videos about this subject are the bests.
Thank you for this fantastic and so well explained example! I realized you deserve more then what I gave so adding another gift - your series is priceless - seriously (I have a MS in Physics so I really appreciate your work.)
Why is the energy of the plane wave in region I the same as the energy of the plane wave in region II? I assume it’s due to conservation of energy but is there no change in energy due to interaction with the potential? Why is my thinking that the plane wave should loose energy when it enters region II wrong?
a unitary operator is one whose hermitian is the same as its inverse. This essentially means it is a "rotation" or "translation" in the abstract Hilbert space of quantum states as if you apply it to vectors within an inner product you do not change the value of the inner product.
I wonder if the "negative probabilities" have anything to do with antimatter? As in, a particle hits the strong barrier and creates some matter and antimatter pairs. Maybe the overall amplitude isn't a probability amplitude, but an "average amplitude" for the number of particles. After all, the "average" number of particles in a region reduces to the probability of finding one, in the case of a one-particle system. Maybe the antimatter counts as a "negative particle."
It IS related to antimatter. If the potential is supercritical then you have enough energy to create particles (or anti-particles) and that is exactly what happens. The density related to the Klein-Gordon wave function is a charge density. For the charge density to be conserved when you have a particle creation (more positive density outside the potential), then you also need to have an antiparticle (more negative density in the potential, because antimatter has oposite charge)
Enjoy my content?
Consider supporting NHU at
patreon.com/nickheumann
If you want to see a specific video topic, you can start or support a petition using ablebees! www.ablebees.com/team/nickheumannuniversity
Also, join our community discords server, where you can ask questions and find other students to study with!
discord.gg/vXJHWvC6MJ
Incredibly detailed, logical as it should be! Thank you for this explanation! Really an outstanding vid.
thank you!!! please keep teaching QFT! you're a blessing
Man, at the end of the video my mind was blowing, thanks a lot for making me understand these things! Grettings from Brasil, I am a master studente in QFT e yours videos about this subject are the bests.
excellent stuff - thanks a lot for your cool work.
great video. still continuing this.
Thanks!
Wow, thanks a lot for the support! It means a lot!
Thank you for this fantastic and so well explained example! I realized you deserve more then what I gave so adding another gift - your series is priceless - seriously (I have a MS in Physics so I really appreciate your work.)
You are great.... amazing vedio lecture series..... please make some lectures on nuclear physics and electrodynamic theory...❤🎉🎉
Nice video for QFT beginners..
Nice video
Why is the energy of the plane wave in region I the same as the energy of the plane wave in region II? I assume it’s due to conservation of energy but is there no change in energy due to interaction with the potential? Why is my thinking that the plane wave should loose energy when it enters region II wrong?
I was thinking the exact same thing. Afterall, doesn't the Einstein momentum-energy equation tell us that E'^2 = p'^2 + m^2?
I don't understand how the momentum can have imaginary components. Can you recommend a text book that covers that? Thanks.
What is the meaning that unitarity is violated and unitarity is not violated?
Your comment please.
a unitary operator is one whose hermitian is the same as its inverse. This essentially means it is a "rotation" or "translation" in the abstract Hilbert space of quantum states as if you apply it to vectors within an inner product you do not change the value of the inner product.
I wonder if the "negative probabilities" have anything to do with antimatter? As in, a particle hits the strong barrier and creates some matter and antimatter pairs. Maybe the overall amplitude isn't a probability amplitude, but an "average amplitude" for the number of particles. After all, the "average" number of particles in a region reduces to the probability of finding one, in the case of a one-particle system. Maybe the antimatter counts as a "negative particle."
Very interesting point! I guess you will *not* be surprised in a few lectures by what we discuss
It IS related to antimatter. If the potential is supercritical then you have enough energy to create particles (or anti-particles) and that is exactly what happens.
The density related to the Klein-Gordon wave function is a charge density. For the charge density to be conserved when you have a particle creation (more positive density outside the potential), then you also need to have an antiparticle (more negative density in the potential, because antimatter has oposite charge)
wow❤
Thank you 🙏
Thanks!
Thank you for the support!