A particle in an infinite square well is a theoretical model used in quantum mechanics to study the behavior of a particle confined to a one-dimensional box with infinitely high potential walls on either side.
The properties of a particle in an infinite square well include a discrete energy spectrum, meaning the particle can only have certain energy levels, and a probability distribution that is confined to the well and decreases towards the walls.
The energy of a particle in an infinite square well is directly proportional to its wavelength. This is known as the de Broglie relation and is given by the equation E = (n^2*h^2)/(8mL^2), where n is the quantum number, h is Planck's constant, m is the mass of the particle, and L is the length of the well.
The wave function in a particle in an infinite square well represents the probability amplitude of finding the particle at a specific position within the well. It also describes the energy states and behavior of the particle within the well.
A particle in an infinite square well is confined to a specific region and has a discrete energy spectrum, while a free particle can move freely and has a continuous energy spectrum. Additionally, the wave function for a particle in an infinite square well is zero at the walls, while a free particle's wave function extends to infinity.