Position and Momentum Spaces in Quantum Mechanics
Further information: Momentum operatorIn 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 And Momentum Space
Famous quotes containing the words position, spaces, quantum and/or mechanics:
“Will women find themselves in the same position they have always been? Or do we see liberation as solving the conditions of women in our society?... If we continue to shy away from this problem we will not be able to solve it after independence. But if we can say that our first priority is the emancipation of women, we will become free as members of an oppressed community.”
—Ruth Mompati (b. 1925)
“In any case, raw aggression is thought to be the peculiar province of men, as nurturing is the peculiar province of women.... The psychologist Erik Erikson discovered that, while little girls playing with blocks generally create pleasant interior spaces and attractive entrances, little boys are inclined to pile up the blocks as high as they can and then watch them fall down: “the contemplation of ruins,” Erikson observes, “is a masculine specialty.””
—Joyce Carol Oates (b. 1938)
“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)
“the moderate Aristotelian city
Of darning and the Eight-Fifteen, where Euclid’s geometry
And Newton’s mechanics would account for our experience,
And the kitchen table exists because I scrub it.”
—W.H. (Wystan Hugh)