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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).
In quantum mechanics, dynamical pictures (or representations) are the multiple equivalent ways to mathematically formulate the dynamics of a quantum system.. The two most important ones are the Heisenberg picture and the Schrödinger picture.
By utilizing the interaction picture, one can use time-dependent perturbation theory to find the effect of H 1,I, [15]: 355ff e.g., in the derivation of Fermi's golden rule, [15]: 359–363 or the Dyson series [15]: 355–357 in quantum field theory: in 1947, Shin'ichirō Tomonaga and Julian Schwinger appreciated that covariant perturbation ...
In the more common Schrödinger picture, even the states of free particles change over time: typically the phase changes at a rate that depends on their energy. In the alternative Heisenberg picture, state vectors are kept constant, at the price of having the operators (in particular the observables) be time-dependent. The interaction picture ...
The phenomenology of quantum physics arose roughly between 1895 and 1915, and for the 10 to 15 years before the development of quantum mechanics (around 1925) physicists continued to think of quantum theory within the confines of what is now called classical physics, and in particular within the same mathematical structures.
The example above could also have been analyzed in the interaction picture. The following example, however, is more difficult to analyze without the general formulation of unitary transformations. Consider two harmonic oscillators , between which we would like to engineer a beam splitter interaction,
In mathematical physics, some approaches to quantum field theory are more popular than others. For historical reasons, the Schrödinger representation is less favored than Fock space methods. In the early days of quantum field theory , maintaining symmetries such as Lorentz invariance , displaying them manifestly, and proving renormalisation ...
The following derivation [4] makes use of the Trotter product formula, which states that for self-adjoint operators A and B (satisfying certain technical conditions), we have (+) = (/ /), even if A and B do not commute.