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In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters ψ and Ψ (lower-case and capital psi, respectively). Wave functions are complex-valued. For example, a wave function might assign a complex ...
The function s(x, t) is often called the source function because in practice it describes the effects of the sources of waves on the medium carrying them. Physical examples of source functions include the force driving a wave on a string, or the charge or current density in the Lorenz gauge of electromagnetism.
Consequently, the wave function also became a four-component function, governed by the Dirac equation that, in free space, read (+ (= )) =. This has again the form of the Schrödinger equation, with the time derivative of the wave function being given by a Hamiltonian operator acting upon the wave function.
For example, the fundamental ... Superposition of three oscillating dipoles- illustrate the time propagation of the common wave function for different n,l,m. We ...
In representing the wave function of a localized particle, the wave packet is often taken to have a Gaussian shape and is called a Gaussian wave packet. [25] [26] [27] Gaussian wave packets also are used to analyze water waves. [28] For example, a Gaussian wavefunction ψ might take the form: [29]
For example, the wave function with =, = has the same energy as the wave function with =, =. This situation is called degeneracy and for the case where exactly two degenerate wave functions have the same energy that energy level is said to be doubly degenerate. Degeneracy results from symmetry in the system.
A wave function for a single electron on 5d atomic orbital of a hydrogen atom. The solid body shows the places where the electron's probability density is above a certain value (here 0.02 nm −3): this is calculated from the probability amplitude. The hue on the colored surface shows the complex phase of the wave function.
In non-relativistic quantum mechanics, the probability current j of the wave function Ψ of a particle of mass m in one dimension is defined as [2] = = {} = {}, where ℏ {\displaystyle \hbar } is the reduced Planck constant ;