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So, we'll pick up with that, with some of the solutions and starting to talk about energies on Friday.
会去解薛定谔方程的某个方面，我们在周五,将从一些薛定谔方程的解开始。
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The radius of the orbit, the energy of the system and the velocity of the electron, I am just going to present you the solutions.
是轨道的半径，系统的能量,以及电子的速度，我接下来会给你们讲解其方程的解法。
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We're going to be looking at the solutions to the Schrodinger equation for a hydrogen atom, and specifically we'll be looking at the binding energy of the electron to the nucleus.
我们将研究下氢原子薛定谔方程的解,特别是电子和核子的结合能,我们将研究这部分。
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So you should drop the homework before you come into class, rather than furiously work on it during class, and the solutions will be posted the same afternoon.
所以你应该在进教室之前交作业,而不是在上课的时候乱写一通,作业答案会在当天下午发布到网上
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And when you have an optimal substructure and the local solutions overlap, that's when you can bring dynamic programming to bear.
当你得到一个最优子结构,但局部解决方案有重跌时，你就可以引入动态编程,来解决这个问题了。
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The poem then tries out different answers, answers that alternately explore transcendental and secular solutions.
该诗试图给出不同的回答，答案分别探索,超验和世俗的解决方法。
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We need to think about solutions to this, right from the start of the class, and we already talked about something.
从一上课开始,我们就应该开始,思考这些问题解决方案,现在我们已经谈论了一些了
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And they were kind enough to send us this magnetic tank which we'll call forth from the computer solutions to a series of problems that would occur on a simulated flight to the planet Saturn.
他们很友善，送给我们这个有磁性的水槽,用于计算机解决一系列,土星模拟飞行中,可能出现的问题。
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They say with the contraction in Venture Capital doesn't mean we're not going to get good solutions to the business problems we face.
他们认为风险投资上的契约并不意味着,能有好的方式来解决面临的商业困难。
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These are setups of pieces on the chess board that have particular solutions. And they're very complex, and they have a kind of aesthetic form to them.
象棋有些设置是有专门的,解决方法的，很复杂，它们有一种美学在里面。
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The third group that was given the candies and put in a positive playful mood outperformed the other two groups significantly-- they thought about more options and they actually came up with better solutions with that problem.
第三组得到糖果,并获得积极愉快的心情,明显比另外两组有更好表现-,他们考虑更多选择,得出更好的问题解决办法。
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We'll be using the solutions, so you shouldn't have a problem, but I wanted to point it out so it does not look too strange to you.
我们将会用它的解，所以你们不应该问题，但是我想提出它,这样你们就不会对它太陌生。
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So, we just want to appreciate that what we'll be using in this class is, in fact, the solutions to the Schrodinger equation, and just so you can be fully thankful for not having to necessarily solve these as we jump into the solutions and just knowing that they're out there and you'll get to solve it at some point, hopefully, in your careers.
所以，我们仅仅想要鉴别,将会在这门课中用到的，事实上就是薛定谔方程的解，而且你们可以非常欣慰,因为你们没有必要去,解这些方程而是直接用它们的解,并且知道这些解出自那里,希望你们在学习生涯中。
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You've got the model solutions, and there will be a test in recitation on Tuesday the 14th based upon that homework.
你们也有参考答案，在周二的背诵课上会有个测试,就是14号，基于你们的家庭作业。
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There is a plurality of solutions that conform to the boundary conditions, which is that the system must be bound.
这有许多解决方式,来遵守这个有界条件，那个系统必须是有界的。
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The notion here is that you can get a globally optimal solution from locally optimal solutions to sub-problems.
这里的概念是你可以通过,子问题的局部最优方案,得到全局优化解决方案。
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