Wavefunction

In quantum mechanics, the wavefunction associated with a particle such as an electron, is a complex-valued function ψ defined over a portion of space and normalized in such a way that

Related Topics:
Quantum mechanics - Electron - Complex-valued - Function

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

: int |psi(x)|^2 dx = 1. quad

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In Max Born's probabilistic interpretation of the wavefunction, the amplitude squared of the wavefunction |ψ(x)|2 is the probability density of the particle's position. Thus the probability of finding the particle in a region A of space is

Related Topics:
Max Born - Amplitude - Probability density

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

: operatorname{Pr}(A) = int_A |psi(x)|^2 dx. quad

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In the mathematical formulation of quantum mechanics, the state of any system is represented by an object called a ket, which is an element of an abstract mathematical structure called a Hilbert space. For isolated systems, the dynamics (or time evolution) of the system can be described by a one-parameter group of unitary operators. In a wide class of systems this Hilbert space of kets has one or more realizations as a space of complex-valued functions on some space; in this case we refer to these functions as wavefunctions. However, a priori, there is no preferred representation as a Hilbert space of functions. Moreover, in some of these representations the time evolution of the system has the form of a partial differential equation, namely Schrödinger's equation.

Related Topics:
Mathematical formulation of quantum mechanics - State - Ket - Hilbert space - Dynamics - Time evolution - One-parameter group - Unitary operator - Partial differential equation - Schrödinger's equation

~ ~ ~ ~ ~ ~ ~ ~ ~ ~