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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} .
While in principle this approach to solving quantum dynamics is equivalent to the Schrödinger picture or Heisenberg picture, it allows more easily for the inclusion of incoherent processes, which represent environmental interactions. The density operator has the property that it can represent a classical mixture of quantum states, and is thus ...
In quantum mechanics, the interaction picture (also known as the interaction representation or Dirac picture after Paul Dirac, who introduced it) [1] [2] is an intermediate representation between the Schrödinger picture and the Heisenberg picture.
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.
Summarized below are the various forms the Hamiltonian takes, with the corresponding Schrödinger equations and forms of wavefunction solutions. Notice in the case of one spatial dimension, for one particle, the partial derivative reduces to an ordinary derivative.
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.
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.