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2. Hilbert space - Wikipedia

   en.wikipedia.org/wiki/Hilbert_space

   The name "Hilbert space" was soon adopted by others, for example by Hermann Weyl in his book on quantum mechanics and the theory of groups. [22] The significance of the concept of a Hilbert space was underlined with the realization that it offers one of the best mathematical formulations of quantum mechanics. [23]

3. Quantum state space - Wikipedia

   en.wikipedia.org/wiki/Quantum_state_space

   In quantum mechanics a state space is a separable complex Hilbert space.The dimension of this Hilbert space depends on the system we choose to describe. [1] [2] The different states that could come out of any particular measurement form an orthonormal basis, so any state vector in the state space can be written as a linear combination of these basis vectors.

4. Decoherence-free subspaces - Wikipedia

   en.wikipedia.org/wiki/Decoherence-free_subspaces

   A decoherence-free subspace (DFS) is a subspace of a quantum system's Hilbert space that is invariant to non-unitary dynamics. Alternatively stated, they are a small section of the system Hilbert space where the system is decoupled from the environment and thus its evolution is completely unitary.

5. Dirac–von Neumann axioms - Wikipedia

   en.wikipedia.org/wiki/Dirac–von_Neumann_axioms

   A state of the quantum system is a unit vector of , up to scalar multiples; or equivalently, a ray of the Hilbert space . The expectation value of an observable A for a system in a state ψ {\displaystyle \psi } is given by the inner product ψ , A ψ {\displaystyle \langle \psi ,A\psi \rangle } .

6. Quantum configuration space - Wikipedia

   en.wikipedia.org/wiki/Quantum_configuration_space

   In quantum field theory, it is expected that the Hilbert space is also the space on the configuration space of the field, which is infinite dimensional, with respect to some Borel measure naturally defined. However, it is often hard to define a concrete Borel measure on the classical configuration space, since the integral theory on infinite ...

7. Geometric quantization - Wikipedia

   en.wikipedia.org/wiki/Geometric_quantization

   The quantum (as opposed to prequantum) Hilbert space is the space of sections of that are covariantly constant in the direction of the polarization. [ 4 ] [ b ] The idea is that in the quantum Hilbert space, the sections should be functions of only n {\displaystyle n} variables on the 2 n {\displaystyle 2n} -dimensional classical phase space.

8. Two-state quantum system - Wikipedia

   en.wikipedia.org/wiki/Two-state_quantum_system

   In quantum mechanics, a two-state system (also known as a two-level system) is a quantum system that can exist in any quantum superposition of two independent (physically distinguishable) quantum states. The Hilbert space describing such a system is two-dimensional. Therefore, a complete basis spanning the space will consist of two independent ...

9. Topological quantum field theory - Wikipedia

   en.wikipedia.org/wiki/Topological_quantum_field...

   The space Z(Σ) is the Hilbert space of the quantum theory and a physical theory, with a Hamiltonian H, will have a time evolution operator e itH or an "imaginary time" operator e −tH. The main feature of topological QFTs is that H = 0, which implies that there is no real dynamics or propagation along the cylinder Σ × I .