Creation and annihilation operators are mathematical operators that have widespread applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator lowers the number of particles in a given state by one. A creation operator increases the number of particles in a given state by one, and it is the adjoint of the annihilation operator. In many subfields of physics and chemistry, the use of these operators instead of wavefunctions is known as second quantization.
Creation and annihilation operators can act on states of various types of particles. For example, in quantum chemistry and many-body theory the creation and annihilation operators often act on electron states. They can also refer specifically to the ladder operators for the quantum harmonic oscillator. In the latter case, the raising operator is interpreted as a creation operator, adding a quantum of energy to the oscillator system (similarly for the lowering operator). They can be used to represent phonons.
The mathematics for the creation and annihilation operators for bosons is the same as for the ladder operators of the quantum harmonic oscillator. For example, the commutator of the creation and annihilation operators that are associated with the same boson state equals one, while all other commutators vanish. However, for fermions the mathematics is different, involving anticommutators instead of commutators.
Read more about Creation And Annihilation Operators: Derivation For Quantum Harmonic Oscillator, Matrix Representation, Mathematical Details, Creation and Annihilation Operators For Reaction-diffusion Equations, Creation and Annihilation Operators in Quantum Field Theories
Famous quotes containing the words creation and/or annihilation:
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—Henry David Thoreau (1817–1862)
“How can anyone be interested in war?—that glorious pursuit of annihilation with its ceremonious bellowings and trumpetings over the mangling of human bones and muscles and organs and eyes, its inconceivable agonies which could have been prevented by a few well- chosen, reasonable words. How, why, did this unnecessary business begin? Why does anyone want to read about it—this redundant human madness which men accept as inevitable?”
—Margaret Anderson (1886–1973)