Final answer:
The wave functional for the vacuum state can be represented as Ψ[ϕ(x)] = exp(-∫(ϕ(x)²/2)dx) in quantum mechanics.
Step-by-step explanation:
Wave functional for vacuum state in terms of field ϕ(x):
In quantum mechanics, the wave function describes the state of a physical system. For the vacuum state, the wave functional can be represented as:
Ψ[ϕ(x)] = exp(-∫(ϕ(x)²/2)dx)
This wave functional gives the probability amplitude for a field configuration ϕ(x) in the vacuum state.