Position operator

In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle. The eigenvalue of the operator is the position vector of the particle.

Introduction

In one dimension, the square modulus of the wave function, , represents the probability density of finding the particle at position . Hence the expected value of a measurement of the position of the particle is

Accordingly, the quantum mechanical operator corresponding to position is , where

The circumflex over the x on the left side indicates an operator, so that this equation may be read The result of the operator x acting on any function ψ(x) equals x multiplied by ψ(x). Or more simply, the operator x multiplies any function ψ(x) by x.

Eigenstates

The eigenfunctions of the position operator, represented in position space, are Dirac delta functions. To show this, suppose that is an eigenstate of the position operator with eigenvalue . We write the eigenvalue equation in position coordinates,

Position (team sports)

Position in team sports refers to the joint arrangement of a team on its field of play during a game and to the standardized place of any individual player in that arrangement. Much instruction, strategy, and reporting is organized by a set of individual player positions that is standard for the sport.

Some player positions may be official, others unofficial. For example, baseball rules govern the pitcher by that name, but not the shortstop, where pitcher and shortstop are two of baseball's nine fielding positions.

For information about team or player positions in some particular sports, see:

Basketball

Batting sports

Football

Gaelic Sports

Hockey

Position (vector)

In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference origin O. Usually denoted x, r, or s, it corresponds to the straight-line distances along each axis from O to P:

The term "position vector" is used mostly in the fields of differential geometry, mechanics and occasionally vector calculus.

Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces in any number of dimensions.

Definition

Three dimensions

In three dimensions, any set of three dimensional coordinates and their corresponding basis vectors can be used to define the location of a point in space—whichever is the simplest for the task at hand may be used.

Commonly, one uses the familiar Cartesian coordinate system, or sometimes spherical polar coordinates, or cylindrical coordinates;

where t is a parameter, owing to their rectangular or circular symmetry. These different coordinates and corresponding basis vectors represent the same position vector. More general curvilinear coordinates could be used instead, and are in contexts like continuum mechanics and general relativity (in the latter case one needs an additional time coordinate).

Nasty

Nasty may refer to:

In music:

Other uses:

See also

Nasty (album)

Nasty is a live album released by the funk/R&B group Cameo in 1996. In addition to the live material, two new studio tracks were included: "Come Fly With Me" and the album's title track, both written by Larry Blackmon. The "Mega-Mix" is a remix of the album's live tracks. The new studio tracks on this release were the only newly written material released by the band for the next five albums.

Track listing

Nasty (Pixie Lott song)

"Nasty" is a song by English recording artist Pixie Lott from her self-titled third studio album (2014). It was released on 7 March 2014 as the album's lead single by Mercury Records. The accompanying music video was filmed in November 2013 and directed by Bryan Barber. A second version featured British band The Vamps was released in the same day only in United Kingdom and Ireland.

"Nasty" was previously recorded by American singer Christina Aguilera in collaboration with CeeLo Green for inclusion on the soundtrack to the 2010 film Burlesque, which stars Aguilera and Cher, but it was ultimately scrapped from the official track listing due to legal issues concerning sample clearance.

Background

"Nasty" was previously recorded by several artists, including Christina Aguilera, who recorded the song as a duet with CeeLo Green for her debut film project Burlesque (2010). However, their version did not make the final track listing due to legal issues concerning sample clearance. After Lott's legal team managed to clear all of the song's samples, the singer recorded her own version of the song and released it as the first single from her self-titled third studio album. In an interview with Metro, Lott explained, "A few other singers had recorded it and Christina was one of them so everyone wanted this song. When I heard other singers had done it I thought 'I need to get this!' It was a difficult song to get because there are so many old-school samples on it, like James Brown, that are hard to clear copyright on. But I got it and now it is my new single."