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What are some examples of 'pictures' in quantum mechanics besides the famous Schrodinger and Heisenberg pictures?

In the Schrodinger picture, one takes the time evolution operator to be acting on states; in the Heisenberg picture, the observables are taken to evolve unitarily while states remain time-independent.

Since an expectation value is fully determined by a state vector, an observable, and the time evolution operator (given by $\langle \psi|U^{-1}OU|\psi\rangle$), it looks like the above 'pictures' exhaust all possible interpretations as far as expectation values are concerned. If not, what are other possible pictures (i.e, interpretations of expectation values) in quantum mechanics?

Lory
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1 Answers1

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What are some examples of 'pictures' in quantum mechanics besides the famous Schrodinger and Heisenberg pictures?

The other well-known "picture" is called the "Interaction picture."

The Hamiltonian is split into two parts: $$ H = H_0 + V\;, $$ which generally can be quite arbitrary, but usually there is some motivation such as $H_0$ can be solved exactly.

Then, we impart time-dependence to the operators like: $$ \hat A_I = e^{+i\hat H_0 t/\hbar}A_S e^{-i\hat H_0 t/\hbar}\;, $$ which can be compared to the "Heisenberg picture": $$ \hat A_H = e^{+i\hat H t/\hbar}A_S e^{-i\hat H t/\hbar}\;, $$

hft
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