-
And the solution to this equation looks like this where it is written in terms of a quantity called a wavefunction.
这个方程的解法是,看起来像是写成数学符号就是,波函数。
-
The electronic configuration, all it is is the shorthand notation for that one electron approximation for the Schrodinger equation for lithium.
电子构型就是，对于锂的薛定谔方程,的单电子近似的,简化形式。
-
Suppose f of x, y, z equals k1, that is my equation, s1 and it gives me a solution s1.
假设我的方程是这样，然后给出了一个解。
-
We've used the fundamental equations that are hiding down here, out of sight but never out of mind.
我们利用了,写在这里的基本方程，虽然没有注意它但却时时刻刻记者它。
-
You've got to juggle the two equations, multiply that by 4, multiply that by 3, add and subtract and so on.
同时处理这两个方程,这个两边乘以4,另一个两边乘以3,将两方程相加或相减求出答案
-
I want to show you how easy it is to change the code. But, notice, once I've added this I actually have a problem. This is now an under-constrained problem. I have more unknowns than I have equations.
我加上这个条件后,我马上面临一个问题了,这就是现在是一个非约束性问题了,我的未知数比方程数多,你从代数中可以知道。
-
So now I've got actually, that looks like three equations, it's really just two equations, because one of them implies the other.
最后实际上是,看似三个方程,实则只有两个方程,因为其中一个暗示了另一个
-
Let's try it with a different equation of state, that isn't quite as simple as the ideal gas case.
考虑一个不同的状态方程，这状态方程不像理想气体状态方程那么简单。
-
But we can use equations that describe waves to describe matter, and that's what we're going to be doing today.
但我们可以用描述波的方程,来描述物质，这就是我们今天要做的。
-
What he did was took de Broglie motion of the electron as a wave and developed a wave equation for such matter waves.
他所做的就是,用电子的德布罗意运动,作为波并且对于那种物质波,给出波动方程。
-
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。
-
And our job is to find out what is the mathematical description of this path, this line in p-V's case that connects these two point.
我们的任务,就是找出，描述这条曲线的方程。
-
I know I only need 2, so I can relate dV dV to dp through the ideal gas law.
我只需要两个就够了，因此可以用,理想气体状态方程消去。
-
All right. So jumping in to having established that, yes, particles have wave-like behavior, even though no, hey're not actually photons, we can't use that equation.
好的，我们已经承认了，粒子有波动性，虽然它们不是光子，我们不能用这个方程。
-
The Schr?dinger equation will give us the energy levels in molecules.
薛定谔方程会告诉我们,分子中的能级。
-
If you knew only the third derivative of the function, you can have something quadratic in t without changing the outcome.
如果方程里有三阶导数,你就可以引入一个二次项,但是结果却不会变
-
And, if we do so, we can actually get a handle on that Born exponent by solving the equation.
如果我们这样做，我们实际上能够得到波恩指数,通过解这个方程得到。
-
For example, F x y z if I have an equation that looks like this, f of x, y, z.
打个比方，我有个这样的方程。
-
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。
-
All right, so that's what we're going to cover in terms of the energy portion of the Schrodinger equation.
好，这就是我们要讲的,关于薛定谔方程能量的部分。
-
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。
-
And if your answer is no, your answer will be no, then you just know you can't use this equation here.
如果不是，那就不能，你就知道，你不能用这个方程了。
-
So, anything on the left side of the equation is called a reactant, and anything on the right side of the equation is called a product.
在方程的左边的,都称为反应物，在方程右边的,都称为产物。
-
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。
-
So, what we can do instead of talking about the ionization energy, z because that's one of our known quantities, so that we can find z effective.
我们做的事可以代替讨论电离能,因为那是我们知道的量子数之一，那是我们可以解出有效的，如果我们重新排列这个方程。
-
For real gases, there's a whole bunch of equation the states that you can find in textbooks, and I'm just going to go through a few of them.
这是理想气体的状态方程,对实际气体,你可以在教科书里，找到许多描述它们的,状态方程。
-
Also, when we're looking at the Schrodinger equation, it allows us to explain a stable hydrogen atom, which is something that classical mechanics did not allow us to do.
当我们看一个薛定谔方程的时候，它给出一个稳定的氢原子,这是在经典力学中做不到的。
-
But luckily for us, there's a classical equation of motion that will, in fact, describe how the electron and nucleus change position or change their radius as a function of time.
但幸运的是，有一个,经典方程描述了电子和核子,位置或者它们直接的距离是,如何随时间变化的。
-
We can't actually go ahead and derive this equation of the wave function squared, because no one ever derived it, it's just an interpretation, but it's an interpretation that works essentially perfectly.
从这个方程中,导出，波函数的平方，没有人可以这样做，这仅仅是一种解释，但这种解释，能解释的很好，自从它第一次被提出来之后。
-
So there's going to be a line that's going to connect the initial point to the final point, and that line mathematically is not going to be the same as this one here.
连接绝热过程,初末态的曲线的方程，和等温线的方程,也不会相同。
应用推荐