Question

A particle is in a one-dimensional box of length l (i.e. the box spans from x = 0 to x = l). The wavefunction for this particle can be described as?

Answer 1

The wavefunction for a particle in a one-dimensional box of length l is given by sinusoidal functions representing standing waves. The wavefunction is Ψn(x) = √(2/l) sin(nπx/l),

Step-by-step explanation:

The wavefunction for a particle in a one-dimensional box of length l (i.e., the box spans from x = 0 to x = l) can be described using Schrödinger's equation for a particle in an infinite potential well. In quantum mechanics, such a system is referred to as the 'infinite square well'. The wavefunction in this scenario is given by sinusoidal functions that represent standing waves within the box. These standing waves only occur at certain wavelengths that fit an integer number of half wave cycles in the length l.

For a particle of mass m, the wavefunctions are:

• Ψn(x) = √(2/l) sin(nπx/l),

where n is the quantum number representing different energy levels.