Position and Momentum 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 And Momentum Space

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

    “It is in vain that we would circumscribe the power of one half of our race, and that half by far the most important and influential. If they exert it not for good, they will for evil; if they advance not knowledge, they will perpetuate ignorance. Let women stand where they may in the scale of improvement, their position decides that of the race.”
    —Frances Wright (1795–1852)

    “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)

    “A personality is an indefinite quantum of traits which is subject to constant flux, change, and growth from the birth of the individual in the world to his death. A character, on the other hand, is a fixed and definite quantum of traits which, though it may be interpreted with slight differences from age to age and actor to actor, is nevertheless in its essentials forever fixed.”
    —Hubert C. Heffner (1901–1985)

    “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)