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bobydbcn
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I want to know the projective Hilbert space of coherent state and squeezed state.Thank you very much!
bobydbcn said:I want to know the projective Hilbert space of coherent state and squeezed state.
strangerep said:That question is too vague. If you want a good answer you'll need to put
effort into articulating your question better.
The projective Hilbert space of coherent states is a mathematical concept in quantum mechanics that describes the set of all possible states of a quantum system. It is a complex vector space that represents the quantum states of a system in terms of coherent states, which are eigenstates of the annihilation operator.
The projective Hilbert space of coherent states is a quotient space of the regular Hilbert space, which means it is constructed by identifying certain vectors in the regular Hilbert space that are equivalent. This allows for a more compact representation of quantum states and simplifies calculations in quantum mechanics.
Coherent states have several important properties in quantum mechanics, such as being minimum uncertainty states and exhibiting classical-like behavior. They are also used to describe the dynamics of quantum systems and play a crucial role in quantum optics and quantum information theory.
Coherent states are minimum uncertainty states, which means they have the smallest possible uncertainty in measurements of position and momentum. This is because they are eigenstates of the annihilation operator, which is related to the position operator in quantum mechanics.
Yes, coherent states have been experimentally realized in various physical systems, such as in quantum optics using laser beams, in superconducting circuits, and in trapped ion systems. These experiments have demonstrated the classical-like behavior of coherent states and their usefulness in quantum information processing.