SchrödingerBild

SchrödingerBild is the German-language term for the Schrödinger picture, one of the standard formulations of quantum mechanics. In this representation, the state vectors |ψ(t)⟩ of a quantum system carry the time dependence, while the operators corresponding to observables are constant in time.

Mathematically, the dynamics are governed by the Schrödinger equation iħ ∂t|ψ(t)⟩ = H|ψ(t)⟩, with H the Hamiltonian. For a time-independent H, the solution is |ψ(t)⟩ = U(t,t0)|ψ(t0)⟩ with U = exp(-iH(t-t0)/ħ). Expectation values ⟨ψ(t)|A|ψ(t)⟩ evolve through the state, while A is fixed in this picture. If the Hamiltonian is time-dependent, the evolution is described by the time-ordered exponential U(t,t0) = T exp(-i∫ H(t') dt'/ħ).

SchrödingerBild is physically equivalent to the Heisenberg picture: they yield the same predictions for measurement outcomes, though the time dependence is carried by different elements (states vs. operators). The two pictures are related by a unitary transformation and represent the same underlying dynamics.

Commonly used in nonrelativistic quantum mechanics and quantum chemistry, the SchrödingerBild is a foundational concept for teaching and solving dynamics problems, including particles in potential wells, atoms in external fields, and evolving superpositions.

Alternative German terms include Schrödinger-Darstellung or Schrödingerbild; it is distinct from the Heisenberg picture (Heisenberg-Darstellung) and the interaction picture (Wechselwirkungsdarstellung).