Quantum Mechanics · Chapter 26

Second quantisation and fields

When particles are created and destroyed, or are too many and too identical to label, the state has to say how many occupy each mode instead. Fock space, creation and annihilation operators for bosons and for fermions, operators written through them, the quantised modes of a field, the scalar and the spinor field, and particles as the quanta of fields.

F = n = 0 ⨁ \infty H^{(n)}

a^^{†} ∣ n ⟩ = n + 1 ∣ n + 1 ⟩

N^= i \sum a^_{i}^{†} a^_{i}

ψ^(x) = i \sum a^_{i} ϕ_{i} (x)

Lessons

Build the foundation

07The scalar fieldThe Klein–Gordon equation failed as the equation of one particle and succeeds as the equation of a field.Read lesson →

08The spinor fieldThe Dirac equation, too, becomes the equation of a field.Read lesson →

09Particles as field quantaThe picture the chapter has built: the world is made of fields, and particles are their quanta.Read lesson →

10Chapter practiceBring the chapter together: occupation numbers and Fock space, creation and annihilation operators for bosons and for fermions, one-body operators and bands, quantised modes, the scalar and the spinor field, and particles as the quanta of fields. No worked example sits above the answers.Read lesson →

Mapping the lesson.

Second quantisation and fields

Build the foundation