# Quantum State

In quantum physics, quantum state refers to the state of a quantum system. A quantum state is given as a vector in a vector space, called the state vector. The state vector theoretically contains statistical information about the quantum system. For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant state vector is given by the principal quantum number . For a more complicated case, consider Bohm formulation of EPR experiment, where the state vector involves superposition of joint spin states for 2 different particles.

In a more general usage, a quantum state can be either "pure" or "mixed." The above example is pure. Mathematically, a pure quantum state is represented by a state vector in a vector space, which is a generalization of our more usual three dimensional space. A mixed quantum state corresponds to a probabilistic mixture of pure states; however, different distributions of pure states can generate equivalent (i.e., physically indistinguishable) mixed states. Quantum states, mixed as well as pure, are described by so-called density matrices, although these give probabilities, not densities.

For example, if the spin of an electron is measured in any direction, e.g., with a Stern-Gerlach experiment, there are two possible results, up or down. The vector space for the electron's spin is therefore two-dimensional. A pure state is a two-dimensional complex vector, with a length of one. That is, . A mixed state is a matrix that is Hermitian, positive-definite, and has trace 1.

Before a particular measurement is performed on a quantum system, the theory usually gives only a probability distribution for the outcome, and the form that this distribution takes is completely determined by the quantum state and the observable describing the measurement. These probability distributions arise for both mixed states and pure states: it is impossible in quantum mechanics (unlike classical mechanics) to prepare a state in which all properties of the system are fixed and certain. This is exemplified by the uncertainty principle, and reflects a core difference between classical and quantum physics. Even in quantum theory, however, for every observable there are states that determine its value exactly.

### Other articles related to "quantum, quantum state, quantum states, states, state":

Quantum Tomography
... Quantum tomography or quantum state tomography is the process of reconstructing the quantum state (density matrix) for a source of quantum systems by measurements on the systems coming from the source ... The source may be any device or system which prepares quantum states either consistently into quantum pure states or otherwise into general mixed ... To be able to uniquely identify the state, the measurements must be tomographically complete ...
Color Of Chemicals - Theory
... are capable of absorbing and releasing energy in the form of photons, accompanied by a change of quantum state ... of energy absorbed or released is the difference between the energies of the two quantum states ... There are various types of quantum state, including, for example, the rotational and vibrational states of a molecule ...
Skolian Empire - Science - Quasis
... In interstellar travel, Skolians often make use of quasis, which is a form of quantum-shielding that freezes the quantum state of all particles on a spacecraft ... The quasis prevents change in the quantum state of any particle, temporarily rendering the ship invulnerable ... While in quasis, the quantum state of all the occupants of the ship also freezes causing the crew to experiences the quasis as a disjointed segment of time ...
Quantum State - Formalism in Quantum Physics - Mixed States
... See also Density matrix A pure quantum state is a state which can be described by a single ket vector, as described above ... A mixed quantum state is a statistical ensemble of pure states (see quantum statistical mechanics) ... Equivalently, a mixed-quantum state on a given quantum system described by a Hilbert space naturally arises as a pure quantum state (called a ...
Magnetic Quantum Number - Derivation
... There are a set of quantum numbers associated with the energy states of the atom ... The four quantum numbers n, ℓ, m, and s specify the complete and unique quantum state of a single electron in an atom called its wavefunction or orbital ... that when solved lead to the first three quantum numbers ...

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A state is not a state if it belongs to one man.
Sophocles (497–406/5 B.C.)

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Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)