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classes:2009:fall:phys4101.001:q_a_1007 [2009/10/07 10:13] – x500_spil0049classes:2009:fall:phys4101.001:q_a_1007 [2009/10/13 16:53] (current) – x500_kroh0054
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 In the case of the infinite square well, I understood the particle can be found out in the square well because the energy is larger than potential energy, E>V(x) (0<x<a). That's why we try to get the Shrodinger equation. In the case of the infinite square well, I understood the particle can be found out in the square well because the energy is larger than potential energy, E>V(x) (0<x<a). That's why we try to get the Shrodinger equation.
 Compared to this concept, Could you explain the physical concept of the Schrodinger equation for the Delta function Well? For the bound state, E<0, this means that particle can be found out within the narrow Delta function Well? Compared to this concept, Could you explain the physical concept of the Schrodinger equation for the Delta function Well? For the bound state, E<0, this means that particle can be found out within the narrow Delta function Well?
 +
 +===Daniel Faraday 10/6 12:30===
 +The way I see it, there are two big conceptual differences between the two models:
 +
 +First: For square wells, the //bottom// of the well is at V=0, so for a wavefunction to exist anywhere it has to have E>0. 
 +But for the delta well potential, the energy at the //top// of the delta well is zero, so a particle with E > 0 will not 'bounce off' the well and a particle with E < 0 will bounce off the well (except for quantum tunneling effects, that is).
 +
 +Secondly, for the infinite square well, the particle can only exist in the well because the potential everywhere else is infinite. In other words, <math>\psi(x) = 0</math> outside the well. But for the delta well potential, the wavefunction could have a nonzero value anywhere.
 +
 +In practice, you don't really try to find the value of the wavefunction "in the well". You find the wavefunction on the left side of the well, and also on the right side of the well, and use boundary conditions at the well to find the unknown coefficients of the wavefunctions.
 +
 +I hope that made sense.
 +
 ====Blackbox 19:31 10/06/2009==== ====Blackbox 19:31 10/06/2009====
 I can understand them mathematically. What is the physical meaning of 2.121?  I can understand them mathematically. What is the physical meaning of 2.121? 
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 Correct me, but i think,  Correct me, but i think, 
 In eq. 2.121 this are the same old boundary conditions. The significants of this conditions allow use to understand special case and general problems.#2 is the restriction we apply to the infinite square well to understand the basics of the wave behavior in a simple case and leads to the idea of leakage i believe. However, for #1 of these B.C. should it say ψ is always continues except at points where the potential is infinite? In eq. 2.121 this are the same old boundary conditions. The significants of this conditions allow use to understand special case and general problems.#2 is the restriction we apply to the infinite square well to understand the basics of the wave behavior in a simple case and leads to the idea of leakage i believe. However, for #1 of these B.C. should it say ψ is always continues except at points where the potential is infinite?
 +
 +====Zeno 10/7 10:30AM====
 +On pg. 75 of our text Griffiths reminds us that "it's impossible to create a normalizable free-particle wave function without involving a //range// of energies" so "R and T should be interpreted as the //approximate// reflection and transmission probabilities for particles in the //vicinity// of E." Is there a way to describe R and T in terms of the range of energies specifically? Or are they stuck just being estimates? If they are destined to only approximate the probabilities, how can we be sure of their accuracies?
 +
 +
 +
 +====Zeno 10/7 11AM====
 +One more conceptual question: I understand how particles can penetrate potential barriers, reflecting and transmitting the incident wave, but I don't understand the reflection by a potential //well//. The delta function well in Fig 2.15 has me wondering how a well reflects part of a wave instead of "trapping" it in a bound state or transmitting it. I feel like there's something simple conceptually that I'm missing, so a little help with interpretation would be much appreciated.
 +
 +===chavez 10/8 6PM===
 +It makes sense (to me) if you divide the space under consideration into regions associated with specific potentials. There will then be a discontinuity in the potential energy between each region of space. It is a general property of waves to scatter when a discontinuity in potential is encountered.
 +
 +===Pluto 4ever 10/7 7PM===
 +Essentially, what I get from this is that this deals with the probability of a particle being able to get out of a well. The more energetic a particle is the greater the probability it has of escaping from the well. So if a particle does not have the energy to make it through the barrier then it will be reflected back into the well (trapped). Of course, that is not to say it will never be able to get out. Although, it energy is less than the barrier it can still escape by means of tunneling.
 +
 +===Dark Helmet 10/08===
 +I think of it like waves on a string of different materials.  Any time the wave changes medium there will be both reflection and transmission.  If you think of the potential well as just a part of the string that is less dense and a wall as part that is more dense, it makes sense.  Anytime the wave changes potentials, it's like the string changing mediums.  At least that's how i think of it, but i could be missing something too. 
 +===spillane===
 +Are there other resources that explain the delta function and the associated limit of a sequence. 
 +
 +====Dagny====
 +When we have a delta-function barrier, why do we no longer have a bound state?
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classes/2009/fall/phys4101.001/q_a_1007.1254928437.txt.gz · Last modified: 2009/10/07 10:13 by x500_spil0049

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