Quantum One
Identical Particles
Creation and Annihilation Operators for Identical Particles
In this segment we introduced the notion of Fock Space, which is the direct sum of the state spaces associated with different numbers of identical particles. In the process, we introduce separately for bosons and fermions, annihilation and creation operators that take particles out of the single particle states that they are in, or put them into (possibly other) single particle states. The number operator for a given single particle state, can now be viewed as a product of the creation and annihilation operators for that state. To “count”, is then equivalent to taking a particle out and putting it back into the same single particle state. Similarly, by taking products of creation and annihilation operators for different single particle states it is possible to form operators that induce transitions, i.e., operators which take a particle out of one state, and put it back into a different state. The following segments explore in more detail how this works.
In this segment we introduced the notion of Fock Space, which is the direct sum of the state spaces associated with different numbers of identical particles. In the process, we introduce separately for bosons and fermions, annihilation and creation operators that take particles out of the single particle states that they are in, or put them into (possibly other) single particle states. The number operator for a given single particle state, can now be viewed as a product of the creation and annihilation operators for that state. To “count”, is then equivalent to taking a particle out and putting it back into the same single particle state. Similarly, by taking products of creation and annihilation operators for different single particle states it is possible to form operators that induce transitions, i.e., operators which take a particle out of one state, and put it back into a different state. The following segments explore in more detail how this works.
In this segment we introduced the notion of Fock Space, which is the direct sum of the state spaces associated with different numbers of identical particles. In the process, we introduce separately for bosons and fermions, annihilation and creation operators that take particles out of the single particle states that they are in, or put them into (possibly other) single particle states. The number operator for a given single particle state, can now be viewed as a product of the creation and annihilation operators for that state. To “count”, is then equivalent to taking a particle out and putting it back into the same single particle state. Similarly, by taking products of creation and annihilation operators for different single particle states it is possible to form operators that induce transitions, i.e., operators which take a particle out of one state, and put it back into a different state. The following segments explore in more detail how this works.
In this segment we introduced the notion of Fock Space, which is the direct sum of the state spaces associated with different numbers of identical particles. In the process, we introduce separately for bosons and fermions, annihilation and creation operators that take particles out of the single particle states that they are in, or put them into (possibly other) single particle states. The number operator for a given single particle state, can now be viewed as a product of the creation and annihilation operators for that state. To “count”, is then equivalent to taking a particle out and putting it back into the same single particle state. Similarly, by taking products of creation and annihilation operators for different single particle states it is possible to form operators that induce transitions, i.e., operators which take a particle out of one state, and put it back into a different state. The following segments explore in more detail how this works.
In this segment we introduced the notion of Fock Space, which is the direct sum of the state spaces associated with different numbers of identical particles. In the process, we introduce separately for bosons and fermions, annihilation and creation operators that take particles out of the single particle states that they are in, or put them into (possibly other) single particle states. The number operator for a given single particle state, can now be viewed as a product of the creation and annihilation operators for that state. To “count”, is then equivalent to taking a particle out and putting it back into the same single particle state. Similarly, by taking products of creation and annihilation operators for different single particle states it is possible to form operators that induce transitions, i.e., operators which take a particle out of one state, and put it back into a different state. The following segments explore in more detail how this works.