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I need help with 1-D step potential problem.
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| Dr. Z |
I know some of you have probably taken Quantum because of all the engineers and who-knows-what people on this board.
I need to know the main difference between the classical (physics) behaviour of the transmission coefficient and the quantum-mechancial.
I know that the classical transmission coefficient goes to unity discontinuously as E -> Vo. E being the energy of the particle, and Vo the potential of the step.
And the Transmission is continous as E -> Vo in the quantum mechanical sense. What is a more important difference then what I have said right above?
:conf: |
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| Dr. Z |
My assignment is due tomorrow, plz help!
:nervous: |
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| Endlesswave |
| :( Sorry man, I'm an English major, post in chillout as well, maybe you'll get more responses? |
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| DJ_Science |
| This is probably way to late, but I just saw this post. The transmission coefficient doesn't really exist in the classical sense. Your only get transmission through a potential well through particle tunneling which is a quantum mechanical event. The only place i can think of where you would have to deal with tranmission in a classical sense is for EM waves propogating through a solid. Are you trying to draw a comparison between the two? |
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| DJ_Science |
| Unless of course E is greater the Vo, then you no longer have a potential barrier and what i said can be somewhat modified. |
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| Rocco |
what the HELL is going on?
i'll probably review this thread a good 4 years from now |
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| Dr. Z |
No worries.
I got it.
Basically when you are plotting Transmission vs. Energy of particle, there are 3 regions of the function.
One is when the energy is smaller then the potential. In this case, the function increases almost exponentially as opposed to the classical sense where there would be no transmission at all. It would be a zero at all points lower than the potential. Since the function has an energy term at the denominator it will explode when energy is a certain value, in this case potential, its just how the function is. So you have to take the limit as the energy approaches that value.
In this case, it gives you a real value. After that, the energy is higher than the potential. In the classical sense the particle would just pass freely, but in the quantum mechanical, it asymptotes at 1 transmission. Which is basically the same as classical.
So yea, I just had to understand how the two functions connect at the E=Vo. |
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| dEsidEL |
long live the TOTA manfest~! Dr. Z i hope u get ur questions answered by the 12843712894723 engineers here .. DigiNutZ where are you
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