Now Isaac Newton and/or Joseph Raphson figured out how to do this kind of thing for all differentiable functions.
既然牛顿和拉复生已经,指数了如何解这种可导函数,因此我们就不用太担心了。
We looked at the wave functions, we know the other part of solving the Schrodinger equation is to solve for the binding energy of electrons to the nucleus, so let's take a look at those.
我们看过波函数,我们知道解,薛定谔方程的其他部分,就是解对于原子核的电子结合能,所以我们来看一看。
psi The solution of the Schr?dinger equation is psi, a wavefunction.
那薛定谔方程的解是什么,是,一个波函数。
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。
And on Monday what we were discussing was the solution to the Schrodinger equation for the wave function.
周一我们讨论了,薛定谔方程解的波函数。
psi I mentioned that we can also solve for psi here, which is the wave function, and we're running a little short on time,
我说过我们也可以解,波函数,我们讲的稍微有点慢,
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。
And we also, when we solved or we looked at the solution to that Schrodinger equation, what we saw was that we actually needed three different quantum numbers to fully describe the wave function of a hydrogen atom or to fully describe an orbital.
此外,当我们解波函数,或者考虑薛定谔方程的结果时,我们看到的确3个不同的量子数,完全刻画了氢原子,的波函数或者说轨道。
I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.
我还没有给你们看过,氢原子波函数的解,让我现在给你们看一下,然后再来说,概率密度,实际上,对于任何一个波函数来说,我们可以把它,分解为两部分,分别叫做径向波函数,和角向波函数。
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