Résumé
Creation operators 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 (usually denoted ) lowers the number of particles in a given state by one. A creation operator (usually denoted ) 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. They were introduced by Paul Dirac. 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. Constructing Hamiltonians using these operators has the advantage that the theory automatically satisfies the cluster decomposition theorem. 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. Quantum harmonic oscillator#Ladder operator method In the context of the quantum harmonic oscillator, one reinterprets the ladder operators as creation and annihilation operators, adding or subtracting fixed quanta of energy to the oscillator system. Creation/annihilation operators are different for bosons (integer spin) and fermions (half-integer spin).
À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.
Cours associés (21)
PHYS-432: Quantum field theory II
The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions such as Quantum Electrodynamics.
PHYS-454: Quantum optics and quantum information
This lecture describes advanced concepts and applications of quantum optics. It emphasizes the connection with ongoing research, and with the fast growing field of quantum technologies. The topics cov
PHYS-431: Quantum field theory I
The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.
Afficher plus
Séances de cours associées (100)
Physique quantique I
Couvre les bases de la physique quantique, en se concentrant sur l'oscillateur harmonique quantique et les kets propres de hamiltonien.
Modèles Hubbard : Formalisme de la matrice de densité
Couvre les modèles Hubbard et le formalisme de matrice de densité en mécanique quantique.
Opérations quantiques
Couvre les opérations quantiques, l'espace Fock, les opérateurs de création et d'annihilation, et la quantification des opérations.
Afficher plus
MOOCs associés (1)
Cavity Quantum Optomechanics
Fundamentals of optomechanics. Basic principles, recent developments and applications.