Operators in Quantum Mechanics

[Guest alexepascual]

I can see how you can bracket an operator with a state vector and get the expectation value of the observable represented by the operator. This would be like getting a weighted average of the different eigenvalues (which are the possible measurement outcomes).

What I don't understand is the meaning of multiplying an operator times a state vector. You would get the eigenvalues multiplied times the components of the vector (for each eigenstate), and I don't see what use could be made of this information.

Something I understand much less is the physical meaning of multiplying two operators together.

i'll appreciate your comments.

[Guest alexepascual]

When I wrote the previous post I was thinking about a hermitean operator that has been diagonalized and a state vector expressed in the eigenbasis of the operator.

If I expressed my idea incorrectly I appologize. I am just someone trying to understand quantum mechanics, and I have a long way to go.

I am hoping there are some people visiting this forum who have an interest in learning more about quantum mechanics, and who have done a little study of the math behind it.

On a side note, I think most books on quantum mechanics don't do such a good job in explaining the connection between the math and the phenomena that is being represented with the math.

If you are studying quantum mechanics on your own or taking a course and would like to share ideas and/or questions, I invite you to join this forum. Let's build some critical mass of people with some basic math background who are genuinely interested in learning.

Thanks,

Alex

[JustinM.Dragna]

Hello, I am also pursuing an understanding of quantum mechanics. I definetly agree that all of the textbooks i have seen give poor explanations of the mathematics behind quantum mechanics, but then again they are physics books. It still doesn't help poor, confused souls like us. I am currently trying to wade my way through Griffiths. I hear it's one of the better books for people without a lot of math background. He dedicates a full chapter to explaining linear algebra. I didn't really find it particularly enlightening, but I'm not much of a mathematician so it could just be me. Anyway, I've been searching around for some good books. If you stumble upon any key me in.

 

-Justin

[bloodhound]

i think getting another book just for linear algebra, instead of relying on one chapter in the quantum mech book would be a good idea.

[Guest alexepascual]

Justin and Bloodhound,

After I didn't get an initial response to my post I stopped checking and I hadn't set the thread t send me email notification. That's why I didn't respond to your messages.

There may not be a very good book in quantum mechanics. I have used several at the same time as some books explain certain topics better than others. I also found a forum where there are a few guys who are very good at the subject and answer my questions when I get stuck.

This forum (scienceforums) does not seem to be very good for quantum mechanics. It appears to be geared more to general science.

The other forum I found has a sub-forum on quantum mechanics and there is a lot of traffic. The name of the site is physicsforums. It uses the same forum engine as this one. They look very similar.

I have found particularly useful Shankar and Sakurai. About Skurai, I have to warn youn that it has many typografical mistakes, but the general approach is better than other books.

I think the books that start off with Dirac notation are better as they take you deeper into the subject without overwhelming you with integrations.

You do have to study linear algebra though.

Griffiths is the book I used for my undergrad courses and I don't like it. The reason is that instead of deriving everything, it assigns many derivations as exercises. It doesn't appear that making the subject easy for the reader has been one of the goals of the authors.

So maybe I'll see you some time at the physicsforums, (remember to go to the quantum mechanics subforum)

Good luck,

-Alex Pascual-

[Dave]

This forum (scienceforums) does not seem to be very good for quantum mechanics. It appears to be geared more to general science.

 

Hence the name And I daresay why physics forums is called that also.

[bloodhound]

I had a look at the introduce urself thread in the general discussions. and there seems to be a few learned physists in there. unfortunately they dont seem to post much

[Dave]

There are quite a few on the forums - swansont and Martin definately know their stuff - but being a general science forum, we're only going to have a few people in a specific area. Maybe as we grow, we'll attract more people who know what we're talking about.