Probability density of generalized coordinate

Yang Xiu-hui

At first it is pointed out that only in the coordinate representation can the probability density of any state for a particle under any potentials generally fulfills the continuum equation.Then the matrix representation of the continuum equation of probability density is presented by virtue of the probability density matrix,the differential operator matrix and the matrix of probability current density vector configured in the coordinate representation,and some discussions are given.

Carl M. Bender, Daniel W. Hook, Peter N. Meisinger +1 more

V. Kapsa, Lubomír Skála

It is shown that Hamilton's principle of classical mechanics can be derived from the relativistic invariance of the generalized spacetime Fisher information corresponding to the statistical description of results of measurement of the coordinates and the motion in space by means of the probability density and probability density current.

Stanley Gudder

F. J. Arranz, F. Borondo, R. M. Benito

Wen-Fa Lu

Within the framework of thermofield dynamics, we construct a thermalized coherent thermal state, which is a general type of the coherent state with the thermal effects and can be presumably produced experimentally. The wavefunction and the density matrix element in the coordinate repersentation are calculated, and furthermore we give the probability densities, average values and variances of the position, momentum and particle number, which in special cases are consistent with those in the literature. All calculations are performed in the coordinate representation.