Perhaps it would be good for people to share their reflections about QM as comments here. These could focus on what seems most compelling and interested to you, what you would like to remember in 10 years or so or ...?
PS. Please look at the previous post (from today) also.
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7 comments:
For myself, I am rather taken with the kinetic energy. How it resists confinement and how it plays a key role in establishing the size of the atom (through the conflict with potential energy). I think it (K.E.) is also important to molecular binding. With reference to our poll, I think that Sabra has some results that suggest "a", in our "simple molecule" problem, is less than 1 and I think that that is the case also for the optimal (lowest energy) state for H+. This is a little surprising, and was only the view of a small minority in our poll. Does anyone have any ideas on how that might come about?*
Also, i am kind of fascinated by the consequences of sp hybridization in terms of allowing the creation of a variety of wave-functions with interesting spatial orientations. Some related questions I am pondering: What is the nature of the bonding in C60 (60 carbon atoms forming a "buckyball")? What is the nature of a "double bond"?
In terms of class topics, I was most fascinated by the methodologies employed in this course. The use of Perturbation Theory and Variational Calculations opens up a whole new realm of quantum mechanical problems. I was amazed first that perturbation theory actually worked (in finding perturbed states/energies) with some reliability. Furthering this notion, I was even more amazed that the idea of guessing a wavefunction (variational) would actually yield reasonable results. I would like to have both these skills, especially the ability to perform variational calculations in ten years.
I think I was most interested in the ideas behind chemical bonding and our ability to find appropriate combinations of wavefunctions to yield the conditions of sp2 hybridization. I would like to be able to explore this idea more and apply it to known molecules, even simple ones, carrying the calculations through for different geometries, ie sp3, etc.
I also am interested in the nature of double bonds. I know that initially, a single sigma bond forms and then a pi bond forms from p orbitals that begin almost parallel and seem to bend over to meet one another, forming the double bond. I would like to look into this more and see exactly how this happens.
I agree with Nathan about variational calculations. It's an amazing process that is extremely useful. After all, we did use this process to derive our framework for chemical bonding and onward.
I really enjoyed the style of the class. It was refreshing to have a class taught solely by the Socratic Method. We really did learn a lot more than we would have had this been a standard lecture-based class.
I hope everybody's studying and finals go well. Are we all planning to meet up Thursday night? For our pizza/beer party?
Good luck to everybody on their finals.
If I distinguish between what I learned about quantum mechanics and which methods we used, I would say that the most remarkable result about quantum mechanics is the 'struggle' between kinetic and potential energy to determine the ideal value of the spatial extent of the wavefunction, for example. We obtained this result by variational calculation and it turns out that this is a appropriate procedure to find ground state wavefunctions of complicated problems by just combining solutions of exactly solvable problems and minimizing the total energy.
In terms of methods, I think that pertubation theory is a very important technique to remember. It is not only restricted to quantum mechanics, it is quite general.
I think these are the most important issues to keep in mind from this class.
I hope finals are going quite well for you all. Good luck for the remaing ones!
I dont know if anyone is still reading this...but good luck to the relativity kids, and anyone else still trying to stuff their brains. I would like to second Bobby's request for a pizza/beer gathering. Possibly someplace like Woodstock's? They have great pizza and reasonable beer prices during happy hour. It seems pointless to go to Rocker's if it isn't Tuesday. Just my thoughts. As a verklempt Mike Myers would say..."Talk amongst yourselves."
hooray for group work! hehe
yes, the wild and wooly world of variational calculations! scrounging around for as many states as may be viable, shove 'em all together, then see how well they all mix - pretty crazy stuff hahaha
yeah pizza!
pizza would be awesome I think.
order some pepperoni with a small perturbation of mushroom perhaps...
lol
In addition to some of the topics mentioned above such as perturbation theory and variation calculation, which are clearly very useful and for which I appreciate touching on in the group/discussion setting that we did, I was intrigued by the combination of one dimensional states for higher dimensional problems, the splitting of degeneracies, and node counting. The pictoral logic of addition of wave functions was particularly of interest to me, it allows quick qualitative understanding of wave functions of exited states of 2 and 3 dimensional problems as well as a way to view bonding and problems in solid state.
For example, a 4-leaf clover shape can be made by combining two full period functions in the above way, these full periods have one node and corresponds to the first exited state of a 1D infinite square well, but multiplying them together gives solutions which are in the second exited state of the 2D infinite square well. The sum of the nodes of the 1D states used gives the exited state of the 2D problem, and each node in each 1D state corresponds to a line of nodes in the 2D state.
-Sam
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