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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).
The Schrödinger picture is useful when dealing with a time-independent Hamiltonian H, ... For example, consider the operators x(t 1), x(t 2), p(t 1) and p(t 2). The ...
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.
This is the Schrödinger equation for the state vector, and this time-dependent change of basis amounts to transformation to the Schrödinger picture, with x|ψ = ψ(x). In quantum mechanics in the Heisenberg picture the state vector, |ψ does not change with time, while an observable A satisfies the Heisenberg equation of motion,
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 ...
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]
The Schrödinger picture provides a satisfactory account of time evolution of state for a quantum mechanical system under certain assumptions. These assumptions include The system is non-relativistic; The system is isolated. The Schrödinger picture for time evolution has several mathematically equivalent formulations.
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.