Quantum mind by physicists, some of which regard the "alive and dead" cat superposition as quite real. Schrödinger's famous thought experiment poses the question, ""when" does a quantum system stop existing as a superposition of states and become one or the other?" In the same way, it is possible to ask whether the brain's act of making a decision is analogous to having a superposition of states of two decision outcomes, so that making a decision means "opening the box" to reduce the brain from a combination of states to one state. But even Schrödinger didn't think this really happened to the
Sum rule in quantum mechanics to construct operator equalities, which are then applied to the particles or energy levels of a system. Assume that the Hamiltonian formula_1 has a complete set of eigenfunctions formula_2 with eigenvalues formula_3: For the Hermitian operator formula_5 we define the repeated commutator formula_6 iteratively by: The operator formula_8 is Hermitian since formula_5 is defined to be Hermitian. The operator formula_10 is anti-Hermitian: By induction one finds: and also For a Hermitian operator we have Using this relation we derive: The result can be written as For formula_17 this gives: See oscillator strength. Sum rule in quantum mechanics In quantum mechanics,