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creepypasta13

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So this concept of H = H_o + H_int has been extremely confusing to me. Wikipedia offers the best explanation, but there a couple things that still confuses me

http://en.wikipedia.org/wiki/Interaction_picture

Why is the state vector in the Interacting picture defined as

|[itex]\psi[/itex][itex]_{I}[/itex](t)> = e[itex]^{i H_{O,S}t/h}[/itex]|[itex]\psi[/itex][itex]_{S}[/itex](t)>

instead of

|[itex]\psi[/itex][itex]_{I}[/itex](t)> = e[itex]^{i H_{O,S}t/h+ i H_{1,S}t/h}[/itex]|[itex]\psi[/itex][itex]_{S}[/itex](t)>?

why isn't the schrodinger picture of the perturbation included?

Similary, why isn't the schrodinger picture of the perturbation included for the equation of the Operators in the Interaction picture?

Finally, why does the exponential factor that determines the perturbation Hamiltonian include only a H[itex]_{O,S}[/itex] and not a H[itex]_{1,S}[/itex]

http://en.wikipedia.org/wiki/Interaction_picture

Why is the state vector in the Interacting picture defined as

|[itex]\psi[/itex][itex]_{I}[/itex](t)> = e[itex]^{i H_{O,S}t/h}[/itex]|[itex]\psi[/itex][itex]_{S}[/itex](t)>

instead of

|[itex]\psi[/itex][itex]_{I}[/itex](t)> = e[itex]^{i H_{O,S}t/h+ i H_{1,S}t/h}[/itex]|[itex]\psi[/itex][itex]_{S}[/itex](t)>?

why isn't the schrodinger picture of the perturbation included?

Similary, why isn't the schrodinger picture of the perturbation included for the equation of the Operators in the Interaction picture?

Finally, why does the exponential factor that determines the perturbation Hamiltonian include only a H[itex]_{O,S}[/itex] and not a H[itex]_{1,S}[/itex]

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