There's one hbar too many in there, no?christianjb said:w = hbar^2 k^2 / 2m
The Schrodinger equation is a fundamental equation in quantum mechanics that describes how the wave function of a particle evolves over time. It represents the fundamental relationship between the observable properties of a physical system and the underlying wave function.
The Schrodinger equation can be solved for the form of a plane wave by substituting the plane wave solution into the equation and finding the values of the wave vector and energy that satisfy the equation. This results in a mathematical expression for the plane wave, which can then be used to describe the behavior of a particle in a quantum system.
The wave vector in a plane wave represents the direction and magnitude of the wave’s propagation. It is a vector quantity that is perpendicular to the wave front and indicates the direction in which the wave is traveling.
The form of a plane wave is directly related to the probability of finding a particle in a specific location. The square of the amplitude of the wave function is proportional to the probability density of finding the particle at a given point in space. This means that the intensity of the plane wave corresponds to the probability of finding the particle at a particular location.
The Schrodinger equation and the form of a plane wave can be used to describe the behavior of particles in most quantum systems. However, for more complex systems, such as those with multiple particles or interactions, more advanced mathematical methods may be needed to accurately describe the system. Additionally, the Schrodinger equation is limited to non-relativistic systems and does not account for the effects of special relativity.