[xir]

Hi everyone, my chemical mind is having a hard time with a concept of quantum formalism


Could anyone help me understand the relationship between functions and vectors.

i.e if you have a function describing a p orbital and you evaluate it using the vector maths inherent to quantum mechanics how do they link.


Specifically I'm trying to link a function (which i visualise as a line) used to represent the shape of an orbital with vectors (which I visualise as a series of specific numbers). The two concepts don't appear to be comparable as far as I can comprehend.




Any and all help is welcome


Cheers

[renge ishyo]

You probably don't need vectors to describe behavior along a one-dimensional line (scalars will do just fine for that), but if you are going to handle multi-dimensional objects then you are going to need to use vector math to track the given values along each separate axis. For example, for a p-orbital, you have to specify values along each of three spatial dimensions to describe its spatial relationships accurately (since a p-orbital manifests itself as a three dimensional object when visualized).

There are basic quantum mechanical problems used to introduce the topic that avoid vector math, such as the one dimensional particle in a box problem, but these problems lack reality. To get a more complete description of a p-orbital the mathematics are necessarily more complicated.