# Maths used in Quantum physics, specifically particle physics

• B
• ChrisisC
In summary, physics is based on experiments and measurements, and mathematics is used as a language to describe physical models. The specific mathematical tools used are chosen based on their suitability for solving certain problems, and calculus is often necessary in physics problems. For a better understanding of why certain mathematical tools are used, it is recommended to study specific problems and their solutions.
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.)

ChrisisC said:
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.

fresh_42 said:
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.

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.

ChrisisC said:
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. )

bhobba

## 1. What is the role of mathematics in quantum physics?

Mathematics is an essential tool in understanding and describing the behavior of particles in quantum physics. It provides a precise and quantitative framework for modeling and predicting the behavior of particles at the quantum level.

## 2. What are the main mathematical concepts used in particle physics?

Some of the key mathematical concepts used in particle physics include linear algebra, differential equations, complex numbers, and group theory. These concepts are used to describe the properties and interactions of particles at the quantum level.

## 3. How is mathematics used to describe the behavior of particles in quantum physics?

In quantum physics, mathematics is used to construct models and equations that describe the behavior of particles. These models and equations are then used to make predictions about the behavior of particles in different situations and to test the accuracy of the theories.

## 4. How does mathematics help us understand the fundamental laws of nature in particle physics?

Mathematics allows us to formulate and solve equations that describe the fundamental laws of nature, such as the laws of conservation of energy and momentum. These laws are crucial in understanding the behavior of particles at the quantum level and how they interact with each other.

## 5. What are some challenges in using mathematics to study particle physics?

One of the main challenges in using mathematics in particle physics is the complexity of the equations and models needed to describe the behavior of particles at the quantum level. Additionally, there may be limitations in our current mathematical understanding, leading to the need for new mathematical techniques and concepts to be developed and applied in particle physics.

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