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In physics, the Schrödinger picture or Schrödinger representation is a formulation of quantum mechanics in which the state vectors evolve in time, but the operators (observables and others) are mostly constant with respect to time (an exception is the Hamiltonian which may change if the potential changes).
All three of these choices are valid; the first gives the Schrödinger picture, the second the Heisenberg picture, and the third the interaction picture. The Schrödinger picture is useful when dealing with a time-independent Hamiltonian H , that is, ∂ t H = 0 {\displaystyle \partial _{t}H=0} .
This implies that a Schrödinger picture is always available. Matrix mechanics easily extends to many degrees of freedom in a natural way. Each degree of freedom has a separate X operator and a separate effective differential operator P , and the wavefunction is a function of all the possible eigenvalues of the independent commuting X variables.
Any possible choice of parts will yield a valid interaction picture; but in order for the interaction picture to be useful in simplifying the analysis of a problem, the parts will typically be chosen so that H 0,S is well understood and exactly solvable, while H 1,S contains some harder-to-analyze perturbation to this system.
In the Schrödinger picture, a purely quantum channel is a map between density matrices acting on and with the following properties: [2] As required by postulates of quantum mechanics, Φ {\displaystyle \Phi } needs to be linear.
It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. [1] The quantum harmonic oscillator (and hence the coherent states) arise in the quantum theory of a wide range of physical systems. [2]
Commutator relations may look different than in the Schrödinger picture, because of the time dependence of operators. For example, consider the operators x(t 1), x(t 2), p(t 1) and p(t 2). The time evolution of those operators depends on the Hamiltonian of the system.
In the Schrödinger picture, the unitary operators are taken to act upon the system's quantum state, whereas in the Heisenberg picture, the time dependence is incorporated into the observables instead.