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A particle is said to be in a bound state if it remains localized in a bounded region of space ... A pure quantum state is a state which can be described by a single ...
The particle state is more precisely characterized by the associated projective Hilbert space, also called ray space, since two vectors that differ by a nonzero scalar factor correspond to the same physical quantum state represented by a ray in Hilbert space, which is an equivalence class in and, under the natural projection map , an element of .
The spin state is a discrete degree of freedom; quantum state spaces can have continuous degrees of freedom. For example, a particle in one space dimension has one degree of freedom ranging from − ∞ {\displaystyle -\infty } to ∞ {\displaystyle \infty } .
A quantum state for an imperfectly isolated system will generally evolve to be entangled with the quantum state for the environment. Consequently, even if the system's initial state is pure, the state at a later time, found by taking the partial trace of the joint system-environment state, will be mixed. This phenomenon of entanglement produced ...
Since the state space of such a particle is the tensor product of the state spaces associated with the individual one-dimensional wave functions, the time-independent Schrödinger equation for such a system is given by- (+ +) + (+ +) =
A quantum state in the Fock space is called a Fock state if it is an element of the occupancy number basis. A Fock state satisfies an important criterion: for each i, the state is an eigenstate of the particle number operator ^ corresponding to the i-th elementary state k i. The corresponding eigenvalue gives the number of particles in the state.
More precisely, the state of a system is given by a linear combination of all the eigenfunctions of the Schrödinger equation governing that system. An example is a qubit used in quantum information processing. A qubit state is most generally a superposition of the basis states | and | :
A bound state is a composite of two or more fundamental building blocks, ... Consider the one-particle Schrödinger equation. If a state has energy < ...