wavefunction

(noun)

a mathematical function describing the propagation of the quantum mechanical wave associated with a particle (or system of particles), related to the probability of finding the particle in a particular region of space

Related Terms

(noun)

A mathematical function that describes the propagation of the quantum mechanical wave associated with a particle (or system of particles), related to the probability of finding the particle in a particular region of space.

Related Terms

Examples of wavefunction in the following topics:

  • Particle in a Box

    • The potential function (V) is time-independent, while the wavefunction itself is time- dependent.
    • The wavefunction must vanish everywhere beyond the edges of the box, as the potential outside of the box is infinite.
    • Furthermore, the amplitude of the wavefunction also may not "jump" abruptly from one point to the next.
    • These two conditions are only satisfied by wavefunctions with the form:
    • Negative values are neglected, since they give wavefunctions identical to the positive solutions except for a physically unimportant sign change.

  • Wave Equation for the Hydrogen Atom

    • In addition to mathematical expressions for total angular momentum and angular momentum projection of wavefunctions, an expression for the radial dependence of the wavefunctions must be found.
    • The wavefunction itself is expressed in spherical polar coordinates:

  • The Pauli Exclusion Principle

    • The Pauli exclusion principle states that no two fermions can have identical wavefunctions.

  • Description of the Hydrogen Atom

    • In addition to mathematical expressions for total angular momentum and angular momentum projection of wavefunctions, an expression for the radial dependence of the wave functions must be found.

  • The Phase of Orbitals

    • The quantity that is varying ("waving") is a number denoted by ψ (psi), whose value varies from point to point according to the wavefunction for that particular orbital.