Direct Product of Two Spin-Up Vectors: What Is It?

In summary, the conversation discusses direct products in the context of vectors and explains that the direct product of two spin-up vectors is represented by | 1 >. The speaker clarifies that the notation used is not mathematically accurate and that the total z angular momentum of the direct product is 1hbar.
  • #1
dyn
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Hi
I have just started looking at direct products and came across the following which i don't understand :

the direct product of two spin -up vectors = | 1 > which is in a bigger vector space

I don't understand how the direct product is | 1 > ? and in this case is it always a bigger vector space or the same size as the original vector spaces ?
 
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  • #2
That's just sloppy notation. If you are trying to understand direct product, it's basically just making an ordered pair of the two vectors.
|up1> x |up2> = |up1, up2>
Now clearly, the total z angular momentum of |up1, up2> is 1hbar so we can also label this state |1>. But that's just notation, not math.
 

What is a direct product of two spin-up vectors?

A direct product of two spin-up vectors is a mathematical operation that combines two vectors with spin-up states into a single vector. This operation is commonly used in quantum mechanics to describe the state of a system with two spin-1/2 particles.

How is a direct product of two spin-up vectors represented?

In mathematics, a direct product of two spin-up vectors is represented using the tensor product symbol, ⊗. For example, the direct product of two spin-up vectors, |↑⟩ and |↑⟩, would be written as |↑⟩ ⊗ |↑⟩.

What is the significance of a direct product of two spin-up vectors?

The direct product of two spin-up vectors is significant because it allows us to describe the state of a system with two spin-1/2 particles. This is important in understanding the behavior of quantum systems and in making predictions about their properties.

Can a direct product of two spin-up vectors be measured in experiments?

No, a direct product of two spin-up vectors cannot be measured directly in experiments. Instead, it is used as a mathematical tool to describe the state of a system with two spin-1/2 particles. However, the individual spin states can be measured experimentally.

Are there any other types of direct products in physics?

Yes, there are other types of direct products in physics, such as the direct product of two position vectors or two momentum vectors. These direct products are used to describe the state of a system in classical mechanics, while the direct product of two spin-up vectors is used in quantum mechanics.

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