# Linear Algebra thats needed in QM?

• RasslinGod
In summary, you will need LA for QM, but you don't need to know all of the the theorems and properties. You will be able to learn what you need in an undergraduate QM class.
RasslinGod
Hi,

so I am currently taking LA + Diff. eqtns in one class right now. I am planning to take QM in the summer.

So I am wondering, how much of LA is needed for QM? My reason for askign this is that there are so many theorems and properties of matricis that i honestly can't master all of them, and i have difficulty understanding the proofs of many theorems. I'm wondering how much QM uses LA?

What are the topics that i need to have down solidly?
Also, are DE important in QM?

You'll going to use matrices and that eigenvalues/eigenvectors stuff quite a bit. IMO, I say I used more LA than DE in QM

Well, I don't know what your LA class covers, but eigenvalues and eigenvectors are important. Hamiltonian operators are nice to know, same with Hermitian Operators.

In reality, I think a lot of the LA you see will be knowing the language. I don't think anyone expects you to maser LA, but it's important to be comfortable speaking in those terms used in LA.

LA and Diff EQ's are important for QM, but I wouldn't worry too much. I had over a year's break between LA and QM and I still remembered enough to feel comfortable in the class.

Only the very basics will be used, things like taking a determinant, eigenvalues, eigenvectors, etc. The nice thing about QM is that all of your operators are Hermitian, so that limits what you will potentially use. Overall it's not that bad.

As for Diff EQ's, I've only had to "use" it a few times, and it was only in derivations. I've never had to actually use it to solve a problem. Well, none of the really complicated stuff. What you usually do is separation of variables, which is pretty easy, and solve from there.

They usually teach you all the LA you need in an advanced undergraduate QM class. All you need to get by is sophomore level LA. I've found that in QM, I learn a lot of LA without even being aware that I'm learning LA. I actually took an LA course after senior quantum. Every couple of days I'd find myself saying, "hey, I know about that!" So I don't think it's that important to worry about mastering LA before studying quantum. You need to know the basics, like matrix multiplication, linear operators, eigenstuff, etc. But that's about it.

## 1. What is linear algebra and why is it important in quantum mechanics?

Linear algebra is a branch of mathematics that deals with linear equations and their representations in vector spaces. It is important in quantum mechanics because it provides a mathematical framework for understanding the behavior of quantum systems, which can be described using linear equations.

## 2. What are the basic concepts of linear algebra used in quantum mechanics?

Some basic concepts of linear algebra used in quantum mechanics include vector spaces, matrices, eigenvalues and eigenvectors, and inner product spaces. These concepts are used to represent quantum states, operators, and measurements.

## 3. How are matrices used in quantum mechanics?

Matrices are used in quantum mechanics to represent operators that act on quantum states. These operators can represent physical quantities such as position, momentum, and energy, and their corresponding measurements.

## 4. What is the role of eigenvalues and eigenvectors in quantum mechanics?

In quantum mechanics, eigenvalues and eigenvectors are used to represent the possible outcomes and corresponding states of a measurement. The eigenvalues represent the possible measurement values, while the eigenvectors represent the corresponding states that the system can collapse into after the measurement.

## 5. How does linear algebra help in solving problems in quantum mechanics?

Linear algebra provides a powerful tool for solving problems in quantum mechanics. By representing quantum systems and measurements using linear equations, we can use techniques such as matrix algebra and eigenvalue calculations to solve for the behavior of the system and predict measurement outcomes.

Replies
16
Views
477
Replies
9
Views
2K
Replies
13
Views
6K
Replies
6
Views
4K
Replies
5
Views
2K
Replies
16
Views
1K
Replies
4
Views
1K
Replies
2
Views
820