Representation of interaction
The representation of interaction or representation of Dirac of quantum mechanics is a manner of dealing with the problems depending on time.
Condition for application of the representation of interactionIn the representation of interaction, one applies the following assumptions:
One considers a Hamiltonien having the form according to:
- the clean states are dependant on time
- the operators are also dependant on time
- the dynamics of the states is described according to the representation of Schrödinger while the dynamics of the operators is described according to the Représentation of Heisenberg.
- the representation of Dirac applies effectively only to certain problems. The example more speaking is that of the disturbances depending on time.
PropagatorsIn order to recognize that one works in the representation of interaction, the states and the operators will be followed index " I" (like interaction). The direction of this representation holds in what the dependence in time had with will be taken into account in the explicit dependence of observable according to time and the dependence in time which had with in the development of the function of wave. It is another way of describing same physics. This means that the significant physical sizes are unchanged.
There are two operators of evolution in time:
the operator " normal" relating to the Hamiltonian complet
- the operator relating to the nondisturbed Hamiltonian
Definition of the Hamiltonians and function of wave of interaction
The operator depend on time is written as in the representation of Heisenberg
Equations of evolution of the function of wave and the observable onesThe evolution of the function of state is written in this representation:
This equation is known under the name of equation of Schwinger - Tomonaga . The evolution of the physical size represented by the operator has is written:
- A. Messiah, Mechanical Quantum (Dunod)
- J.L. Basdevant, quantum Course of mechanics of the polytechnic school (Ellipses)
- J.J. Sakurai and S.F. Tuan, Modern Mechanics Quantum, Benjamin-Cummings 1985, Reading, Addison-Wesley 2003
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