Heisenberg's & Schrodinger's Picture

  • Thread starter Eynstone
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Is the Heisenberg's picture really equivalent to Schrodinger's ?
It may seem so at a first glance & both produce the same results.But space & time are treated equally in Heisenberg's formulation : the operators are time dependent.In Schrodinger's formulation, states are time-dependent while the hamiltonian may be time-independent. This makes the former congruous & adaptable to relativity.
Also, the initial state vector remains fixed & operators move in Heisenberg's formulation. The initial state is not of so great a consequence as in Schrodinger's picture. Hence, it is more congruous with quantum field theory .(When particle creation & annihilation is involved, we can't work with a state vector in a Hilbert space).
I wonder how the two become totally compatible in the non-relativistic formulation.
 

DrClaude

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It is easy to show mathematically that the two pictures give equal results.

A simple ways to visualize it is to consider that the Schrödinger picture corresponds to a lab-fixed reference frame, in which the state of the quantum system will evolve, while the Heisenberg picture corresponds to a system-fixed reference frame, where the state remains unchanged but the world around (including measuring apparatuses) move as a function of time.
 

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