Why do we use the Tensor Product of Hilbert Spaces?

Asked Jul 29 '23 at 13:46

Active Jul 29 '23 at 13:52

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What is the reason that we use the tensor product of two Hilbert Spaces in order to describe a two-particle system in quantum mechanics?

So what is the precise reason to use the tensor product and not for example a direct sum of Hilbert spaces in order to describe a two-particle system?

edited Jul 29 '23 at 13:52

Qmechanic

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asked Jul 29 '23 at 13:46

Mac Menders

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Does this answer your question? Should it be obvious that independent quantum states are composed by taking the tensor product? – Tobias Fünke Jul 29 '23 at 13:50
Related : Total spin of two spin- 1/2 particles. – Frobenius Jul 29 '23 at 19:47

Why do we use the Tensor Product of Hilbert Spaces?

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