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1 Switching pictures

To switch into the interaction picture, we divide the Schrödinger picture Hamiltonian into two parts, H = H₀ + H₁. Then the state vector is defined as:

Operators transform between the pictures as

.

The Schrödinger equation then becomes in this picture:

The purpose of this picture is to shunt all the time dependence due to H₀ onto the operators, leaving only H_{1, I} affecting the time-dependence of the state vectors.

The interaction picture is conveniant when considering the effect of a small interaction term, H₁, being added to the Hamiltonian of a solved system, H₀. By switching into the interaction picture, you can use time-dependent perturbation theory to find the effect of H_{1, I}.

2 References

• Townsend, John S. (2000). A Modern Approach to Quantum Mechanics (2nd ed.). Sausalito, CA: University Science Books. BooksEnthsiast.com.

3 See also

• Bra-ket notation
• Schrödinger equation