Position Space - Position and Momentum Spaces in Quantum Mechanics

Position and Momentum Spaces in Quantum Mechanics

Further information: Momentum operator

In quantum physics, a particle is described by a quantum state. This quantum state can be represented as a superposition (i.e. a linear combination as a weighted sum) of basis states. In principle one is free to choose the set of basis states, as long as they span the space. If one chooses the eigenfunctions of the position operator as a set of basis functions, one speaks of a state as a wave function ψ(r) in position space (our ordinary notion of space in terms of length). The familiar Schrödinger equation in terms of the position r is an example of quantum mechanics in the position representation.

By choosing the eigenfunctions of a different operator as a set of basis functions, one can arrive at a number of different representations of the same state. If one picks the eigenfunctions of the momentum operator as a set of basis functions, the resulting wave function φ(k) is said to be the wave function in momentum space.

Read more about this topic:  Position Space

Famous quotes containing the words position and, position, spaces, quantum and/or mechanics:

    “There is a certain relief in change, even though it be from bad to worse; as I have found in travelling in a stage- coach, that it is often a comfort to shift one’s position and be bruised in a new place.”
    —Washington Irving (1783–1859)

    “Einstein is loved because he is gentle, respected because he is wise. Relativity being not for most of us, we elevate its author to a position somewhere between Edison, who gave us a tangible gleam, and God, who gave us the difficult dark and the hope of penetrating it.”
    —E.B. (Elwyn Brooks)

    “When I consider the short duration of my life, swallowed up in the eternity before and after, the little space which I fill and even can see, engulfed in the infinite immensity of spaces of which I am ignorant and which know me not, I am frightened and am astonished at being here rather than there. For there is no reason why here rather than there, why now rather than then.”
    —Blaise Pascal (1623–1662)

    “But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
    —Antonin Artaud (1896–1948)

    “It is only the impossible that is possible for God. He has given over the possible to the mechanics of matter and the autonomy of his creatures.”
    —Simone Weil (1909–1943)