Date: 2023-11-12 | Article ID: 22792 |

Article 30983 showed that the model of a free scalar quantum field includes states that behave like localized particles. This article shows that the same model includes states that behave more like classical waves. This article also derives two examples of how the field is affected by an **external source**, an entity that influences the field but is not influenced by the field. (This is used as an easy approximation to a more complete – but also more difficult – model in which the influences go both ways.) One example shows that a time-independent source is surrounded by a "force field," analogous to the static electric field that surrounds a point charge in electrodynamics. Another example shows that a time-dependent source generates a state of the quantum field that behaves like a classical wave.

**2023-11-12**(replaced Hamiltonian with hamiltonian)**2022-10-22**(first version)

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