Statistical Physics | Position space | Momentum space


Statistical Physics

If there are small number particle then their equation of motion may be solved using Newton’s law of motion then they are known as microscopic system and the solution technique dynamical variable technique
Statistical Physics | Position space | Momentum space
Statistical Physics | Position space | Momentum space

If there are large number of particle the equation of motion of all these particle may not be solved simultaneously due to our mathematical incapability the collection of large number of particle is called macroscopic system
A gaseous system consist large number of particles hence gaseous system may be solved by macroscopically i.e either emplying thermodynamics or statical mechanicque in thermodynamics kinetic theory of gases and law of thermodynamics is used to determine the thermodynamics variable pressure, volume, temperature, entropy however in statistical mechanicque the problem may be solved either Maxwell Boltzmann Boltzmann Einstein statistical and Fermi drack statics for quantum particle

Position space

It is a real space in which instantinus statics state of particle having degree of freedom is represented by their position coordinates x,y,z

Momentum space

It is a real space in which instantaneous dynamic state of any particle having three degree of freedom is represented by three momentum coordinates thus for a particle 3D of freedom is represented by the position coordinates x,y,z and three momentum coordinates Px, Py, Pz thus for a three degree of freedom the phase space would be six dimensional space
In figure along x-axis the position coordinates Q the momentum coordinates along y-axis for particle having one degree of freedom is shown

Dimension of phase space

If we have particle having ‘f’ degree of freedom which means that to represented that particle in phase space there must be ‘f’ position coordinates and ‘f’ momentum coordinates therefore in phase space the particle is represented by 2f coordinates hence the phase space would be 2f dimensional
Classification of phase space
There are two type of phase space

(A)   µ-space

To represented a particle having 3D of freedom µ-space may be used in which each particle is represented by a phase point in a six dimensional space therefore in µ-space ‘n’ number of particle are represented by N phase point such that each phase point have three position coordinates and three momentum coordinates

(B)   lambda and gamma-space

In gamma space n-particle (identical) are represented by a single phase point having 3N-position coordinates and 3N-momentum coordinates thus for a three degree of freedom and N-particle gamma space would 6N dimension we can also say that gamma space may be constracted from µ space

Phase point

In a phase space a particle is represented by  position and momentum coordinates with a point called phase point

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