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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} .
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.
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.
The Schrödinger functional is, in its most basic form, the time translation generator of state wavefunctionals. In layman's terms, it defines how a system of quantum particles evolves through time and what the subsequent systems look like.
Rudolf Schrödinger was born on January 27, 1857, [1] to a Bavarian family who had migrated to Vienna, then a part of the Austro-Hungarian Empire, several generations prior. [4] Schrödinger described his mother as having been "very nice, with cheerful character; she was of poor health and helpless towards life, but also unassuming." [3]
It has also been simulated in atomic systems that provide analogues of a free Dirac particle. The first such example, in 2010, placed a trapped ion in an environment such that the non-relativistic Schrödinger equation for the ion had the same mathematical form as the Dirac equation (although the physical situation is different).
The Schrödinger–Newton equation, sometimes referred to as the Newton–Schrödinger or Schrödinger–Poisson equation, is a nonlinear modification of the Schrödinger equation with a Newtonian gravitational potential, where the gravitational potential emerges from the treatment of the wave function as a mass density, including a term that represents interaction of a particle with its own ...