Explicit form for representing two spin 1/2 system

In summary, the conversation discusses the possibility of using a special form, such as a Gaussian function, to represent a "two spin 1/2 system" with different states of "proton1 up/down" and "proton2 up/down" in a double potential well scenario.
  • #1
onsagerian
3
0
explicit form for representing "two spin 1/2 system"

Hello,

Are there any explicit forms(functions) for representing a "two spin(1/2) particle system" whose states are "proton1 up / proton2 up", "proton1 up / proton2 down", "proton1 down / proton2 up", "proton1 down / proton2 down"? Can it be a special form such as a "gaussian" type function, for instance?

Thank you in advance.
 
Last edited:
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  • #2


Sorry! You don't have to worry about the original question I've posted. The situation is a proton moving from left to right in a double potential well that interacts with the other proton moving in the same way in another double potential well. So, I guess a linearly combined guassian type wavefunction may be appropriate to describe the given potential wells.
 

FAQ: Explicit form for representing two spin 1/2 system

What is the explicit form for representing two spin 1/2 systems?

The explicit form for representing two spin 1/2 systems is known as the tensor product or direct product. It is denoted as |s1,s2⟩ and represents the state of the first spin system s1 combined with the state of the second spin system s2.

How is the tensor product of two spin 1/2 systems calculated?

The tensor product of two spin 1/2 systems is calculated by multiplying the state vectors of each system. For example, if the first spin system is in state |0⟩ and the second spin system is in state |1⟩, the tensor product would be |0⟩ ⊗ |1⟩ = |01⟩.

What is the significance of the explicit form for representing two spin 1/2 systems?

The explicit form for representing two spin 1/2 systems is significant because it allows for the representation of entangled states, where the state of one system is dependent on the state of the other. This is important in quantum computing and quantum information processing.

Can the explicit form for representing two spin 1/2 systems be extended to multiple spin systems?

Yes, the explicit form for representing two spin 1/2 systems can be extended to multiple spin systems by simply taking the tensor product of each individual spin system's state vectors. For example, a system with 3 spin 1/2 particles would have an explicit form of |s1,s2,s3⟩.

How is the explicit form for representing two spin 1/2 systems related to the Pauli matrices?

The explicit form for representing two spin 1/2 systems is closely related to the Pauli matrices, which are used to represent the spin states of a single particle. The tensor product of two Pauli matrices results in the explicit form for two spin 1/2 systems, allowing for the calculation of spin correlations and entanglement between the two systems.

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