Maths used in Quantum physics, specifically particle physics

[ChrisisC]

What are the main maths used in the mentioned fields of physics? Not just general terms like "Calculus" but more specific maths. Also, what is the logic behind using these to solve problems in physics? Example, why would someone use differential calculus to calculate the probability of a particle tunneling through a barrier? ( i don't know if you would actually use differential calculus to solve a problem like that, I am just trying to present my question better.)

 

[fresh_42]

What are the main maths used in the mentioned fields of physics? Not just general terms like "Calculus" but more specific maths.

I think even the question, which parts are not used, is hardly answerable. Maybe number theory isn't. Lattices on the other hand ...

Also, what is the logic behind using these to solve problems in physics? Example, why would someone use differential calculus to calculate the probability of a particle tunneling through a barrier? ( i don't know if you would actually use differential calculus to solve a problem like that, I am just trying to present my question better.)

Mathematics is simply a convenient language to describe physical models. How would you express physical concepts like velocity, if not as a quotient of position and time difference? It is simply very natural, because physics is based on experiments which are based on measurements. And the moment you measure something you deal with numbers. Those numbers turn in mathematical concepts, the moment you start to think about physical laws, i.e. amount and kind of dependencies among your measured data like velocity.

 

[ChrisisC]

I think even the question, which parts are not used, is hardly answerable. Maybe number theory isn't. Lattices on the other hand ...

Mathematics is simply a convenient language to describe physical models. How would you express physical concepts like velocity, if not as a quotient of position and time difference? It is simply very natural, because physics is based on experiments which are based on measurements. And the moment you measure something you deal with numbers. Those numbers turn in mathematical concepts, the moment you start to think about physical laws, i.e. amount and kind of dependencies among your measured data like velocity.

I understand what you are saying, but the velocity formula is algebra,is it not? I'm asking why the operations related to calculus and other maths are used to find solutions to different problems. I'm in 10th grade and have never been taught quantum physics or advanced math yet so please excuse my lack of knowledge or the lack of clarity in my questions.

 

[PeterDonis]

This is way too general a question for a PF thread. The general answer is that the mathematical tools that are used are chosen because they seem to be suited for the types of problems to which they are applied. But a detailed discussion of that is way beyond the scope of a PF thread. Accordingly, I am closing this thread.

I'm in 10th grade and have never been taught quantum physics or advanced math yet

Unfortunately, the best advice I can give at this point is patience. It takes time to learn all this stuff, and that includes time to understand why the particular mathematical tools that are used were chosen. There is no simple answer that can be put into a thread like this. But eventually you will learn the tools and be able to use them to solve problems, and that will hopefully show you why they are useful.

If you want to try to get a jump on that process, you could pick a reasonably simple problem (such as quantum tunneling through a barrier) and try to find a presentation of how that problem is solved and see if you can understand it. Then, if you had questions, they would be much more specific and would be easier to address within the scope of a PF thread.

(And unfortunately, yes, most physics problems do require calculus. No way to avoid it, much as many people would like to. )