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ArjSiv
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So, say I have a composite hilbert space [tex]H = H_A \otimes H_B[/tex], can I write any operator in H as [tex]U_A \otimes U_B[/tex]?
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ArjSiv said:So, say I have a composite hilbert space [tex]H = H_A \otimes H_B[/tex], can I write any operator in H as [tex]U_A \otimes U_B[/tex]?
A composite Hilbert space is a mathematical space that is created by combining two or more Hilbert spaces together. It is often used in quantum mechanics to represent systems that have multiple degrees of freedom.
Composite Hilbert spaces have all the same properties as regular Hilbert spaces, such as being complete, separable, and possessing an inner product. However, they also have additional properties that arise from the combination of multiple spaces, such as entanglement between the individual spaces.
Operators in composite Hilbert spaces are defined as mappings from one Hilbert space to another. They act on the combined space and can be written as a matrix of operators, with each entry corresponding to a specific combination of states from the individual spaces.
Composite Hilbert spaces are essential in quantum mechanics as they allow for the representation of complex systems that cannot be adequately described in a single Hilbert space. They also play a crucial role in understanding the entanglement of quantum states.
In composite Hilbert spaces, measurements are performed by projecting the combined state onto one of the individual spaces, and then performing a measurement on that space. The result of the measurement is then used to infer information about the entire system.