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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} .
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).
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 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 physics, the Heisenberg picture or Heisenberg representation [1] is a formulation (largely due to Werner Heisenberg in 1925) of quantum mechanics in which observables incorporate a dependency on time, but the states are time-independent. It stands in contrast to the Schrödinger picture in which observables are constant and the states evolve ...
A straightforward way to define the S-matrix begins with considering the interaction picture. [9] Let the Hamiltonian H be split into the free part H 0 and the interaction V, H = H 0 + V. In this picture, the operators behave as free field operators and the state vectors have dynamics according to the interaction V.
If a, b, c, are real numbers (in the ring R), then one has the continuous Heisenberg group H 3 (R).. It is a nilpotent real Lie group of dimension 3.. In addition to the representation as real 3×3 matrices, the continuous Heisenberg group also has several different representations in terms of function spaces.
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]