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- Thread starter Gean Martins
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- #1

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What reading have you got on both things?

- #3

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The Classical phase space allowed me to describe the dynamics of a system by its eigenvalues and eigenvectors, given from a Hamiltonian .

The two dimensional Hilbert Space, its quitely the same thing,but here i work with eigenstates that my system can assume,restricted by rules of this vectorial space ,where my observables are represented by operators acting on eigenstates.

i don't know if i make myself clear,but my question remains : There's no difference between them ?

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[...]The Classical phase space allowed me to describe the dynamics of a system by its eigenvalues and eigenvectors, given from a Hamiltonian .[...]

- #5

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Actually, i wrote this from my previous knowledge acquired from undergraduate course in physics.

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What textbook were you using? Can you give a reference from it that explains where your statement in post #3 comes from?i wrote this from my previous knowledge acquired from undergraduate course in physics.

(And in case it isn't apparent, the reason we are asking is that your description of classical phase space and dynamics doesn't look right; it looks like a description of quantum Hilbert space and dynamics. So it seems like you are confusing the two.)

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A 2-dimensional space (but a symplectic space, not a Hilbert space) describes classical linear dynamics of a single particle in 1 dimension. In contrast, a 2-dimensional Hilbert space describes quantum linear dynamics of a single spin degree of freedom. The interpretation of a vector in the two spaces is also quite different: Each 2-dimensional vector in the classical symplectic space has real coordinates and describes position and momentum of a moving particle, while a 2-dimensional vector in the quantum Hilbert space has complex coordinates and is just a representative of a ray describing a point on the Bloch sphere, corresponding to a pure spin 1/2 state of a particle at rest.

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- #9

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Maybe, i might have expressed badly on my definition of a

I

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