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what is the tensor product's physical significance? I know what it does mathematically, but what does it mean. I have looked on textbooks and wikipedia but i still can't understand the physical signifcance.
The physical signifigance will depend on the particular application.what is the tensor product's physical significance? I know what it does mathematically, but what does it mean. I have looked on textbooks and wikipedia but i still can't understand the physical signifcance.
so for your quantum mechanics example you mean that when you take the tensor product between the spin state and wave function you get the probablity that it could be spin up or spin down, right?As was mentioned previously, the physical significance depends on the application. Maybe this explanation will help.
Let V be a three dimensional vector space with basis {e1,e2,e3}, and let W be a four dimensional vector space with basis {f1,f2,f3,f4}.
Then V tensor W is a 12 dimensional vector space with basis
e1 tensor f1
e1 tensor f2
e1 tensor f3
e1 tensor f4
e2 tensor f1
e2 tensor f2
e2 tensor f3
e2 tensor f4
e3 tensor f1
e3 tensor f2
e3 tensor f3
e3 tensor f4
Furthermore, V direct sum W is a 7 dimensional vector space with basis:
(e1,0)
(e2,0)
(e3,0)
(0,f1)
(0,f2)
(0,f3)
(0,f4)
See the difference?
In Quantum Mechanics, spin is often considered. There is spin up and spin down. Sometimes the spin state is tensored with a wave function. Then, we have
wavefunction tensor spinstate=(wavefunction+,wavefunction-).
-Reverie
fortunately there is no such thing as an,...ayeeeee!