I've never seen such a dedicated channel to make the common public aware about what science really is and how great it is. Keep up the good work Prof! 👍✌️
Out of all the modules that I've learned at university in the past 2 years; this quantum mechanical barrier problem has been one of my favourites and close to my heart. The way you explain the algebra is superb👌 and I love it❤
Thanks! However at 9:49 I think you missed to factor out the “a” when you took out e ^aik which you took out as e^ik however since you multiplier t by t* it didn’t matter as either e^ik . e^-ikx would be cancelled just as would e ^ aik . e ^-aik . Otherwise unless I am wrong minus this minor factoring out error it is a very great explanation much better than MIT lectures! If I am wrong plz correct me!
Thanks man, you saved my life, I had this as a homework problem and spent like five hours trying to work through the algebra to no avail before finding your vid!
Hey, thank you so much. I have a question: At 18:32 you say that for E1. But you do always have to calculate T again for E>V, if you want to plot it for eta>1, right? (as you do in the video) Because to get the first expression for T we used the fact that E
00:11 Quantum tunneling allows particles with less energy than a barrier's height to still have a non-zero probability of crossing it. 03:25 The transmission and reflection coefficients describe the likelihood of a quantum particle passing through or being reflected by a barrier. 06:36 Manipulations on the system of equations lead to expressions for lower case f, lower case g, and lower case t. 09:36 Simplifying the equation by using the definitions of hyperbolic sine and cosine 12:33 The transmission factor T is defined as t star times t. 15:34 The calculation involves squaring a binomial and simplifying the expression. 18:21 R and T coefficients determine the reflection and transmission probabilities of an electron encountering a barrier. 21:11 Quantum tunneling allows particles to traverse barriers with lower energy than the barrier height. 23:52 Transmission and reflection coefficients depend on the particle's energy relative to the barrier height. 26:47 Quantum mechanics has technological applications Crafted by Merlin AI.
hello sir great job i have a doubt in quantum mechanics- in quantum fluctuations energy is created so it violates newton's laws of conservation of energy,right?
As Sandre said, small quanta of energy can appear spontaneously as long as they are annihilated by an antiparticle within the time required by the Heisenburg Uncertainty Principle, or else conservation of energy is violated.
did you do commutators of operators yet? made for some interesting excercises cause its so unintuitive that quantummechanical operators dont commutate like normal numbers do
I’ve always wanted to get into the nitty-gritty of Quantum Mechanics. And I’m having it now, mostly because of your videos (I had previous qualitative understanding of the issues, but not the technical, I mean quantitative, details -that make most of the difference in Science). So, most sincere thanks to you for that. When, around time mark 23:37, you show the transmission and reflection coefficients for case E>V0, the shape of the curves suggested to me interference effects between the width of the barrier and some wave length (associated with the electron?). Can you comment on that?
Old comment but in case you're still wondering to this day lol: The periodic (cyclical) behavior of the T/R coefficients (in the case that the particle has more energy than the barrier, so goes "over" but yet can still bounce back) is a result of the wavefunction only being able to pass through/over the barrier at specific points along its wave, so to speak. The shape of the wave at the barrier must be in line with the shape of a wave that is on the other side. That only occurs at regular points along the wavefunction's wave cycle, so you get that up and down behavior on the graph. A simple analogy: you throw a baseball over the top of a wall and the baseball has some spin to it. There is a robot on the other side that can detect whether that ball is at specific increments of angles, and only allows through those baseballs which are at those specific angle increments in their rotation. Example: If by the time ball reaches the top of the wall, the ball has rotated exactly 30 degrees (more or less) or any multiple of 30 degrees*, then the robot swats it away (reflection). If that ball has rotated by any other angle, it's allowed through. Of course, the robot is invisible and there is actually no robot. But you get the picture hopefully :) The shape of the wavefunction must be in alignment with the expected shape on the other side. I don't know if you could call that "interference" so much as quantization. The allowed states for transmission are many, but there are states which follow a quantization behavior that cause reflection. * Note: The graph clearly shows that the quantization is not as simple as "any multiple of some angle", as the distance between reflection peaks changes over time. Nevertheless, they are quantized in the sense that they follow a periodic behavior where specific energies have the most likely chance of getting reflected.
I'm not sure, but in 20:24 the Dirac's constant / hbar is wrong? Shouldn't it be something around 6.582119569509073*10^(-16)? you use planck constant in eV not Dirac's constant, if I am not wrong.
I always thought of energy as any particles smaller then atoms. But energy not being a substance but. Action with in a subspace. Fit more with spiritualism . Even light . All though have ions electrons also talked about in that matter by both light science and spiritual speaking. .and can you replace word ura for heat . And chee or bio impulses and mean the same thing
Tengo una duda, y es una vez hallado los coeficientes de transmisión y reflexión, que sigue despues, ya se tienen las autoenergías, pero los autovectores no se llegaron a encontrar, porque teniamos el problema que eran 4 ecuaciones y 5 incognitas, esto nos llevo a definir estos coeficientes, se pueden hallar los valores de A,B,C,F y G? Quisiera expresar las funciones de onda con sus valores ya normalizados, pues A*.A+B*.B=1, agradeceria que se pueda resolver esa duda, tal vez no me he dado cuenta de algo y ya tengo la respuesta
Reading the title, being confused af but still clicking on the Video, the Intro makes me feel that I am goin to understand something. That stopped after the first min tho
-15:40 ...." now this is where we get clever " ... You mean .. everything up to this point was not clever.? And I've just watched 10 minutes of Unclever video .. sheeesh
Hahahaha I know what you mean. It used to be a mandatory junior level class in EE at the university. It was taught by a 6’ 2” 280 lb prof with no sense of humor.
Great video. For some people, the following python code may be useful. It plots T and R vs eta: # Ref: th-cam.com/video/kUR98x1tH0c/w-d-xo.html&ab_channel=ProfessorDaveExplains import numpy as np from matplotlib import pyplot as plt L = 1e-9 # [m] m = 9.11e-31 # [kg] hbar = 1.055e-34 # [J s] V0 = 1.6e-18 # [J] N = 200 eta1 = np.linspace(0.01,0.999, N) # EV0 E1 = eta1*V0 E2 = eta2*V0 T1 = np.zeros(N) # EV0 for i in range(N): k1 = np.sqrt(2*m*(V0-E1[i]))/hbar k2 = np.sqrt(2*m*(E2[i]-V0))/hbar T1[i] = 1/(V0**2*np.sinh(k1*L)**2/(4*E1[i]*(V0-E1[i]))+1) T2[i] = 1/(V0**2*np.sin(k2*L)**2/(4*E2[i]*(E2[i]-V0))+1) #print(f"k1 = {k1}, T = {T2[i]}")
![[กูเพิ่งซื้อมึงปิดหนี] 20 นาที ผมรีวิวเกมที่แย่ที่สุดในโลก CONCORD](http://i.ytimg.com/vi/XhC-3q3Ii7I/mqdefault.jpg)
![เปิดใจ พี่ญา คนรุม หลังทัวร์ลง หนักสุดในชีวิต!! l [Nickynachat]](http://i.ytimg.com/vi/2-OJZRtclro/mqdefault.jpg)
I've never seen such a dedicated channel to make the common public aware about what science really is and how great it is. Keep up the good work Prof! 👍✌️
True🙏
So true
I just learned this formally at university. This is a brilliant video of this topic.
Out of all the modules that I've learned at university in the past 2 years; this quantum mechanical barrier problem has been one of my favourites and close to my heart.
The way you explain the algebra is superb👌 and I love it❤
Please continue this series! it's pure gold for students that have to deal with quantum physics courses. Thanks!
oh man i vaguely remember doing these calculations in theoretical physics class 3 like 13 years ago, feels almost nostalgic
Holy fk. Man my highschool and college didn't even try to show us this stuff.
I hated Quantum Mechanics until I saw this video. Thank you so much, the simple explanation of such a (hard to understand) problem is fantastic
Thanks! However at 9:49 I think you missed to factor out the “a” when you took out e ^aik which you took out as e^ik however since you multiplier t by t* it didn’t matter as either e^ik . e^-ikx would be cancelled just as would e ^ aik . e ^-aik . Otherwise unless I am wrong minus this minor factoring out error it is a very great explanation much better than MIT lectures! If I am wrong plz correct me!
i have never found mit lectures very helpful .
Thanks man, you saved my life, I had this as a homework problem and spent like five hours trying to work through the algebra to no avail before finding your vid!
This and the previous video are super in-depth! Professor Dave, thank you so much for doing this!
Hey, thank you so much.
I have a question: At 18:32 you say that for E1. But you do always have to calculate T again for E>V, if you want to plot it for eta>1, right? (as you do in the video) Because to get the first expression for T we used the fact that E
This is the first time I have seen a tutorial like this so I'll watch
this is the cleanest explanation wow
00:11 Quantum tunneling allows particles with less energy than a barrier's height to still have a non-zero probability of crossing it.
03:25 The transmission and reflection coefficients describe the likelihood of a quantum particle passing through or being reflected by a barrier.
06:36 Manipulations on the system of equations lead to expressions for lower case f, lower case g, and lower case t.
09:36 Simplifying the equation by using the definitions of hyperbolic sine and cosine
12:33 The transmission factor T is defined as t star times t.
15:34 The calculation involves squaring a binomial and simplifying the expression.
18:21 R and T coefficients determine the reflection and transmission probabilities of an electron encountering a barrier.
21:11 Quantum tunneling allows particles to traverse barriers with lower energy than the barrier height.
23:52 Transmission and reflection coefficients depend on the particle's energy relative to the barrier height.
26:47 Quantum mechanics has technological applications
Crafted by Merlin AI.
Amazing video broski. Do you mind showing the code you used for graphing the coefficients?
9:46 the common portion has a in it, so the exponential would be something like this e^(ikoa)
I have understand weeks worth of collage content in 20 min. Unbelivable
Thank you, Sir. I wish science could be taught in this simplified way at universities.
Professor Dave saved my day
Thanks for the video! Such a fascinating concept!
Wow thanks Prof Dave!
Thank you so very much!
I got tunneled straight to heaven, after calculating this with you!
a brilliant video
hello sir great job i have a doubt in quantum mechanics-
in quantum fluctuations energy is created so it violates newton's laws of conservation of energy,right?
I'm a Quantum Chemist, let me explain - In quantum mechanics, small quanta of energy can actually appear spontaneously.
As Sandre said, small quanta of energy can appear spontaneously as long as they are annihilated by an antiparticle within the time required by the Heisenburg Uncertainty Principle, or else conservation of energy is violated.
Very helpful! Can't thank you enough!
Thank you for your time and effort.
Who knew learning quantum physics is so fun
did you do commutators of operators yet? made for some interesting excercises cause its so unintuitive that quantummechanical operators dont commutate like normal numbers do
yep that was the first one in this miniseries! like 6 ago, the one on operators in QM
I’ve always wanted to get into the nitty-gritty of Quantum Mechanics. And I’m having it now, mostly because of your videos (I had previous qualitative understanding of the issues, but not the technical, I mean quantitative, details -that make most of the difference in Science). So, most sincere thanks to you for that.
When, around time mark 23:37, you show the transmission and reflection coefficients for case E>V0, the shape of the curves suggested to me interference effects between the width of the barrier and some wave length (associated with the electron?). Can you comment on that?
Old comment but in case you're still wondering to this day lol:
The periodic (cyclical) behavior of the T/R coefficients (in the case that the particle has more energy than the barrier, so goes "over" but yet can still bounce back) is a result of the wavefunction only being able to pass through/over the barrier at specific points along its wave, so to speak. The shape of the wave at the barrier must be in line with the shape of a wave that is on the other side. That only occurs at regular points along the wavefunction's wave cycle, so you get that up and down behavior on the graph.
A simple analogy: you throw a baseball over the top of a wall and the baseball has some spin to it. There is a robot on the other side that can detect whether that ball is at specific increments of angles, and only allows through those baseballs which are at those specific angle increments in their rotation. Example: If by the time ball reaches the top of the wall, the ball has rotated exactly 30 degrees (more or less) or any multiple of 30 degrees*, then the robot swats it away (reflection). If that ball has rotated by any other angle, it's allowed through. Of course, the robot is invisible and there is actually no robot. But you get the picture hopefully :)
The shape of the wavefunction must be in alignment with the expected shape on the other side.
I don't know if you could call that "interference" so much as quantization. The allowed states for transmission are many, but there are states which follow a quantization behavior that cause reflection.
* Note: The graph clearly shows that the quantization is not as simple as "any multiple of some angle", as the distance between reflection peaks changes over time. Nevertheless, they are quantized in the sense that they follow a periodic behavior where specific energies have the most likely chance of getting reflected.
God bless these videos
20:20 - you took the numerical value for h, not h-bar. Such a minor mistake in a great video, but mistake nonetheless!
I'm not sure, but in 20:24 the Dirac's constant / hbar is wrong? Shouldn't it be something around 6.582119569509073*10^(-16)?
you use planck constant in eV not Dirac's constant, if I am not wrong.
This is just amazing . Thankyou so much!
I always thought of energy as any particles smaller then atoms. But energy not being a substance but. Action with in a subspace. Fit more with spiritualism . Even light . All though have ions electrons also talked about in that matter by both light science and spiritual speaking. .and can you replace word ura for heat . And chee or bio impulses and mean the same thing
You should check out my quantum mysticism debunk.
@@ProfessorDaveExplains that's why I came hear to comment about
Well you really should watch that video.
@@ProfessorDaveExplains I did that's why commenting in more recent video
I have been blessed, thank you Jesus
Professor Dave, sorry i dont quite grasp it yet, should it be e^(ik0a) pulled out at 9:46?
yup there is a missing a
although it cancel out very soon, it still make a little confuse XD
As Rodney Dangerfield said in the movie Back to School “the answer is 4?”
Tengo una duda, y es una vez hallado los coeficientes de transmisión y reflexión, que sigue despues, ya se tienen las autoenergías, pero los autovectores no se llegaron a encontrar, porque teniamos el problema que eran 4 ecuaciones y 5 incognitas, esto nos llevo a definir estos coeficientes, se pueden hallar los valores de A,B,C,F y G? Quisiera expresar las funciones de onda con sus valores ya normalizados, pues A*.A+B*.B=1, agradeceria que se pueda resolver esa duda, tal vez no me he dado cuenta de algo y ya tengo la respuesta
Teacher, in 17:59, what happened with Vo^2 on the denominator?
Forgive me, i understended, Vo^2 is Vo*Vo/E = Vo/ņ = 1/E
Great video
could you show how this would change if the barrier was in an infinite quantum well too? like if there were 5 regions instead of 3?
amazing video :)
I wish I was this excited to learn when I was still in high school 😅
Reading the title, being confused af but still clicking on the Video, the Intro makes me feel that I am goin to understand something.
That stopped after the first min tho
🥉
You lasted that long,good work.
Quantam physics my best topics
notation goes crazy
-15:40 ...." now this is where we get clever " ...
You mean .. everything up to this point was not clever.? And I've just watched 10 minutes of Unclever video .. sheeesh
amazing
Nice
🥇
Belissimo
Houuuuuu such a question 😱😱😱😱😱i got scared my god😱😱😱😱🙋🏻♂️
King Man
❤
I experienced flashbacks and PTSD from pchem when I saw this video on my feed.
Hahahaha I know what you mean. It used to be a mandatory junior level class in EE at the university. It was taught by a 6’ 2” 280 lb prof with no sense of humor.
Завтра экзамен в России, ЕГЭ, по химии. Да пребудет с ними сила и знания химического Иисуса
как прошло??
Let's do more political figure
WTF
Great video.
For some people, the following python code may be useful. It plots T and R vs eta:
# Ref: th-cam.com/video/kUR98x1tH0c/w-d-xo.html&ab_channel=ProfessorDaveExplains
import numpy as np
from matplotlib import pyplot as plt
L = 1e-9 # [m]
m = 9.11e-31 # [kg]
hbar = 1.055e-34 # [J s]
V0 = 1.6e-18 # [J]
N = 200
eta1 = np.linspace(0.01,0.999, N) # EV0
E1 = eta1*V0
E2 = eta2*V0
T1 = np.zeros(N) # EV0
for i in range(N):
k1 = np.sqrt(2*m*(V0-E1[i]))/hbar
k2 = np.sqrt(2*m*(E2[i]-V0))/hbar
T1[i] = 1/(V0**2*np.sinh(k1*L)**2/(4*E1[i]*(V0-E1[i]))+1)
T2[i] = 1/(V0**2*np.sin(k2*L)**2/(4*E2[i]*(E2[i]-V0))+1)
#print(f"k1 = {k1}, T = {T2[i]}")
fig, ax = plt.subplots(figsize=(12,9))
ax.plot(eta1, T1, '--b',linewidth=3,label="T (EVo)")
ax.plot(eta1, 1-T1, '--r',linewidth=3,label="R (EVo")
ax.set_xlabel(r'$\eta=E/V_0$)',fontsize=20)
ax.set_ylabel(r'$T, R$',fontsize=20)
ax.tick_params(axis='both', which='major', labelsize=18)
ax.set_title(r'Transmission and Reflection Coefficients', fontsize=28)
ax.grid()
ax.legend(fontsize=18)
plt.show()
fig.tight_layout()
❤