In quantum field theories and many-body problems one works with creation and annihilation operators of quantum states, a i † † and a i . These operators change the eigenvalues of the number operator, N = ∑ ∑ i n i = ∑ ∑ i a i † † a i , by one, in analogy to the harmonic oscillator. The indices (such as i ) represent quantum numbers that label the single-particle states of the system; hence, they are not necessarily single numbers. For example, a tuple of quantum numbers ( n , ℓ ℓ , m , s ) is used to label states in the hydrogen atom.