Quantum mind with a cat in a locked steel chamber, wherein the cat's life or death depended on the state of a radioactive atom, whether it had decayed and emitted radiation or not. According to Schrödinger, the Copenhagen interpretation implies that "the cat remains both alive and dead" until the state has been observed. Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; on the contrary, he intended the example to illustrate the absurdity of the existing view of quantum mechanics. However, since Schrödinger's time, other interpretations of the mathematics of quantum mechanics have been advanced
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,