Microstates in Phase Space - Edubirdie

University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

387

Pages:

6
Author:

Jabin F.

Microstates in Phase Space Dof f=Dof Allowed volume of phase space Volume of single phase cell Ω= Volume of single phase cell Allowed volume of phase space ∫dqdp The number of microstates for sharp value of momentum Ω(P)=The number of microstates for sharp value of momentum P The number of microstates for the momentum lies between (P)=The number of microstates for the momentum lies between P to P+dP The number of microstates for sharp value of energy Ω(E)=The number of microstates for sharp value of energy E The number of microstates for energy lies between (E)=The number of microstates for energy lies between E to E+dE (E)=g(E)dE Density of states The number of energy states (or microstates) per unit energy interval. g(E)=Density of states=The number of energy states (or microstates) per unit energy interval. The number of microstates per unit energy interval Energy interval g(E)= Energy interval The number of microstates per unit energy interval Consider a particle having momentum and energy ⇒Consider a particle having momentum P and energy E⇒ Dof = 3 = f (free particle) Non-rel. free particle having rest mass that is confined in 3-D region of volume Allowed volume of phase space: Fundamental volume of phase space: 4πVp If particle has momentum that lies in the range p+dp, then Allowed volume of phase space: dp If the energy of the particle lies in the range E+dE, then: 2πV(2m =g(E)dE Dof = 3 (Photon) A photon having momentum P and energy E is confined in 3-D space of volume Allowed value of phase space: Ω(P)= Dof = 1 (Non-Relativistic Particle) Consider a particle having momentum P and energy E that is confined in a region of length Allowed volume of phase space: For momentum lies between P+dP & energy lies between Dof = 1 (Photon)

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