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- (en)
- , (en)
- The time evolution of a closed system is described by a unitary transformation on the initial state. (en)
- The wavefunction of a system of N identical particles is either totally symmetric or totally antisymmetric under interchange of any pair of particles. (en)
- The Hilbert space of a composite system is the Hilbert space tensor product of the state spaces associated with the component systems. For a non-relativistic system consisting of a finite number of distinguishable particles, the component systems are the individual particles. (en)
- Every measurable physical quantity is described by a Hermitian operator acting in the state space . This operator is an observable, meaning that its eigenvectors form a basis for . The result of measuring a physical quantity must be one of the eigenvalues of the corresponding observable . (en)
- If the measurement of the physical quantity on the system in the state gives the result , then the state of the system immediately after the measurement is the normalized projection of onto the eigensubspace associated with (en)
- The time evolution of the state vector is governed by the Schrödinger equation, where is the observable associated with the total energy of the system (en)
- by a state vector belonging to a Hilbert space called the state space. (en)
- When the physical quantity is measured on a system in a normalized state , the probability of obtaining an eigenvalue of the corresponding observable is given by the amplitude squared of the appropriate wave function . (en)
- The state of an isolated physical system is represented, at a fixed time (en)
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