The Schrödinger picture of quantum mechanics is a model for dealing with time-dependent problems. The following assumptions are made:
States are generally time-dependent :
Operators can at most explicitly depend on time: the
only exception is the time expansion operator .
The behavior of the system ( dynamics ) is described by the Schrodinger equation : ,
wherein the Hamiltonian is the system.
To indicate that you are in the Schrödinger picture, states and operators are occasionally given the index "S": or
The time-dependent state is given by the state at a fixed point in time and the unitary time evolution operator :
Two other models are the Heisenberg picture and the interaction picture . All models lead to the same expected values . For the expected value of the operator we get in the Schrödinger picture: