Final answer:
In physics, if the angular momentum (ℓ) is initially zero and there's no external torque, then the angular momentum remains zero. In quantum mechanics, for a particle in a box, ℓ might refer to the box's length, and the probability density being zero at both ends (x = 0 and x = ℓ) reflects its boundary conditions.
Step-by-step explanation:
When ℓ = 0 in the context of physics, specifically within the topic of angular momentum, one possibility may be true based on the law of conservation of angular momentum. In a system with no external torque acting on it (Δλ = 0 or net Τ = 0), the angular momentum remains constant. This implies that if the angular momentum was zero at some initial moment, it will remain zero unless acted upon by an external torque. Additionally, when considering wave functions, a probability density that is largest at the midpoint between 0 and ℓ indicates a quantum mechanical system, such as an electron in a one-dimensional box. Here, ℓ may refer to the length of the box, and in this context, the probability density being zero at x = 0 and at x = ℓ follows from the boundary conditions of the wave function of a particle in a potential well.