Particle number operator

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In quantum mechanics, for systems where the total number of particles may not be preserved, the number operator is the observable that counts the number of particles.

The number operator acts on Fock space. Given a Fock state $|\Psi\rangle_\nu$ composed of single-particle basis states $|\phi_i\rangle$ :

$|\Psi\rangle_\nu=|\phi_1,\phi_2,\cdots,\phi_n\rangle_\nu$

with creation and annihilation operators $a^{\dagger}(\phi_i)$ and $a (φ i)$ we define the number operator $\hat{n_i} \ \stackrel{\mathrm{def}}{=}\ a^{\dagger}(\phi_i)a(\phi_i)$ and we have:

$\hat{n_i}|\Psi\rangle_\nu=n_i|\Psi\rangle_\nu$

where $n i$ is the number of particles in state $|\phi_i\rangle$ .

[edit] See also

[edit] References

Bruus, Henrik, Flensberg, Karsten. (2004). Many-body Quantum Theory in Condensed Matter Physics: An Introduction. Oxford University Press. ISBN 0-19-856633-6.
Second quantization notes by Fradkin

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Category: Quantum mechanics

Particle number operator

From Wikipedia, the free encyclopedia

[edit] See also

[edit] References

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