I Physical parameters for spin 1/2 particles

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The discussion centers on understanding "physically relevant real parameters" in the context of quantum systems, particularly for k half-spin electrons. Participants question how these parameters relate to the local and global phases of spin states and their implications for specifying a quantum system. The confusion arises from the lack of clarity in the instructional material provided, which does not adequately explain the relationship between these parameters and the Hilbert space dimensions. There is a request for examples to illustrate the concept better, especially for systems with 2 or 3 electrons. Overall, the thread highlights the need for clearer explanations and examples to grasp the topic effectively.
lazayama
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I am having trouble to understand what it means by "physically relevant real parameters" and how does it help us to specify a quantum system.

Let say, we have a state of k half spin electrons? My guess is about the local phase of the spin, and this would make it 2^k parameters since each electron has 2 parameters?

What am I missing?
 
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Could you give an example of what you mean by parameters here? Perhaps for a system of 2 or 3 electrons.

Are you talking about the dimension of the Hilbert space of spin states?
 
Thanks for helping!
The book I am looking has mentioned something like global phase / local phase but I don't quite understand, and how does it related to physical REAL parameter and also describe the state of k half spin electron quantum system?
 
lazayama said:
The book I am looking
Which book? You will get way better and more helpful answers if we have more context here.
 
This is not a published book but a material our instructor gave us, and there is a problem asking us about this, so I am quite confused.
Sorry about the confusion as well!
 
lazayama said:
I am having trouble to understand what it means by "physically relevant real parameters"

If we are unable to look at what "it" says directly, I have no idea how to help with this. Are the materials you refer to online? Or can you at least quote more context from them?
 

Thread 'Angular Momentum Vector and Its Magnitude'

For the quantum state ##|l,m\rangle= |2,0\rangle## the z-component of angular momentum is zero and ##|L^2|=6 \hbar^2##. According to uncertainty it is impossible to determine the values of ##L_x, L_y, L_z## simultaneously. However, we know that ##L_x## and ## L_y##, like ##L_z##, get the values ##(-2,-1,0,1,2) \hbar##. In other words, for the state ##|2,0\rangle## we have ##\vec{L}=(L_x, L_y,0)## with ##L_x## and ## L_y## one of the values ##(-2,-1,0,1,2) \hbar##. But none of these...
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