Undergrad Physical parameters for spin 1/2 particles

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SUMMARY

The discussion centers on understanding "physically relevant real parameters" in the context of quantum systems, specifically for k half-spin electrons. Participants clarify that each half-spin electron contributes two parameters, leading to a total of 2^k parameters for k electrons. The conversation also touches on the significance of local and global phases in defining quantum states and the dimension of the Hilbert space associated with these spin states. A request for more context regarding the instructional material is made to facilitate better assistance.

PREREQUISITES
  • Quantum mechanics fundamentals
  • Understanding of spin 1/2 particles
  • Knowledge of Hilbert space concepts
  • Familiarity with local and global phase distinctions
NEXT STEPS
  • Study the concept of Hilbert space dimensions in quantum mechanics
  • Explore the role of local and global phases in quantum state representation
  • Investigate the mathematical formulation of spin states for multiple particles
  • Review quantum mechanics textbooks that cover spin systems, such as "Quantum Mechanics: Concepts and Applications" by Nouredine Zettili
USEFUL FOR

Students and educators in quantum mechanics, physicists specializing in quantum systems, and anyone interested in the mathematical representation of spin 1/2 particles.

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 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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