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A particle in a 1-D Hilbert space would have position basis states ## |x \rangle ## where ## \langle x' | x \rangle = \delta(x'-x) ## A 3-D Hilbert space for one particle might have a basis ## | x,y,z \rangle ## where ##\langle x', y', z' | x,y,z \rangle = \delta(x'-x) \delta (y-y') \delta(z-z') ## . Would it be correct to write ## | x,y,z \rangle = | x \rangle \otimes | y \rangle \otimes | z \rangle ## ? Why or why not?
Call the 1-D Hilbert space ## H_1 ## and the 3-D Hilbert space ## H_3 ##. Is this question equivalent to asking is ## H_3 = H_1 \otimes H_1 \otimes H_1 ##?
Call the 1-D Hilbert space ## H_1 ## and the 3-D Hilbert space ## H_3 ##. Is this question equivalent to asking is ## H_3 = H_1 \otimes H_1 \otimes H_1 ##?