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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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But when you solve the Schrodingerequation, you don't get just a set of solutions that are dependent upon one number.
但当你解薛定谔的方程式时，你没得到有一个统一答案的,一系列解决方法。
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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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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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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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Because in an under-constrained problem there could be multiple solutions. So suppose I want to capture all of them or print all of them out.
因为在一个非约束性问题中,可能会有多组答案,所以假设我想把它们,全部获取或者全部输出。
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It can be a spirit of investigating problems deeply and looking for solutions creatively.
它代表着一种,深入探索问题,提出创新性的解决措施的精神。
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So always amazing to us how we go into the problem, our eye or mind can see one class of solutions, but the math will tell you sometimes there are new solutions and you've got to respect it and understand and interpret the unwanted solutions, and this is a simple example where you can follow what the meaning of the second solution is.
解决问题的方式总能让人惊喜不已,我们的眼睛或思想可以看见一类解,但数学有时会告诉你还有新的解,你不能忽视它,而是解释这些不期而至的解,这只是一个简单的例子,由此你可以理解第二个解的意义
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The second thing is, just as in the case of the violin string, the wave equation, as posed by Schrodinger, has a plurality of solutions.
第二，就那个小提琴弦而言，波动方程，被薛定谔所提出的，有许多解法。
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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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And the plurality of solutions have discrete values associated with them.
那许多解法得出,离散的值。
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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 I have two solutions here; one, what would be sort of the obvious sort of hackish or solve it fast solution?
我这里有两个解决方案，一是有没有一个明显的,独创性的，快速地解决方案？
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You get a set of solutions that are dependent upon -These quantum states fall out of the solution to this equation.
你得到一系列的解,这些解依赖于量子状态,和方程解不相干的解。
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And there are lots of solutions that chemists come up with -- there's always new techniques that allow us to do this, and these are just some of the first, and we'll go through them in a little bit of detail here.
的情况下研究或者发现它们,化学家们想出了很多的办法,人们发明新的技术来实现它，这些是最早遇到的一些问题，我们要稍微来,研究下它们的细节。
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What comes out of the math is that the value of k, there are multiple values, there are multiple solutions.
得到的数学结果是k的值，这有多种值，多种解法。
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So, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.
这就是概率密度，但作为,把它当成是，波函数的解，让我们先倒回来一点。
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What does this mean? Linearity of solutions, the elegant way of saying it is superposition holds.
这是什么意思，方程的线性关系，是解决问题的十分漂亮的方法。
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I have a way of exploring the possible solutions.
我有一种探索可能方案的方式方法。
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If you look in your book there's a whole table of different solutions to the Schrodinger equation for several different wave functions.
如果你们看书的话,上面有一整张,许多，不同波函数,薛定谔方程解的表。
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But instead in this chemistry course, I will just tell you the solutions to differential equations. And what we can do is we can start with some initial value of r, and here I write r being ten angstroms. That's a good approximation when we're talking about atoms because that's about the size of and atom.
但在这个课里，我会直接，告诉你们微分方程的解,我们可以给距离r一个初始值,我这里把r取10埃,当我们讨论原子时,这是一个很好的近似,因为原子的尺寸。
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