- #1
Tio Barnabe
Usually textbooks on QM deals with systems with a single feature. For example, we could analyse electron spin. In such case the state vector is a (function?) only of the corresponding "spin variable" for spin, etc...
But suppose I'm interested in say, study about electron spin and also its position. In such a case, the state vector would need to contain information of both spin and position, correct?
How can we proceed in this case? Should we consider spin part as being in a space while position part in another? And make the (appropriate, according to the rules) product between these spaces? If the answer is, yes, I have the following question: What would be the dimension of the resulting product space?
For instance, the electron spin space would be 2 dimensional, while the position space would be 3 dimensional. Would the dimension of the resulting product space be 5?
Also, based on my questions above, if someone could indicate me some good lectures on web about the related math of the Hilbert space, such that I could finely understand how to mathematically describe what I asked, I will appreciate.
I have found excellent books about Hilbert Space in the uni library, but unfortunately none of them deals with the situation above, i.e. the rules, algebra, etc, when we have to consider product spaces.
But suppose I'm interested in say, study about electron spin and also its position. In such a case, the state vector would need to contain information of both spin and position, correct?
How can we proceed in this case? Should we consider spin part as being in a space while position part in another? And make the (appropriate, according to the rules) product between these spaces? If the answer is, yes, I have the following question: What would be the dimension of the resulting product space?
For instance, the electron spin space would be 2 dimensional, while the position space would be 3 dimensional. Would the dimension of the resulting product space be 5?
Also, based on my questions above, if someone could indicate me some good lectures on web about the related math of the Hilbert space, such that I could finely understand how to mathematically describe what I asked, I will appreciate.
I have found excellent books about Hilbert Space in the uni library, but unfortunately none of them deals with the situation above, i.e. the rules, algebra, etc, when we have to consider product spaces.