3) Relativistic Particles Consider a gas of N relativistic particles with Hamiltonian rn n= where c...
Problem 3: (40 points) One-dimensional relativistic gas: Here we consider a non-interacting gas of N relativistic particles in one dimension. The gas is confined in a container of length L, i.e., the coordinate of each particle is limited to 0 <q < L. The energy of the ith particle is given by ε = c (a) Calculate the single particle partition function Z(T,L) for given energy E and particle number N. [12 points] (b) Calculate the average energy E and...
5.Two relativistic particles of mass m crash into each other, fusing to form a particle of mass M, at rest in the lab, with no other particles emitted. Assuming that each mass m particle had (lab frame magnitude) momentum p prior to the collision, evaluate M in terms of m and p. Was momentum conserved in the fusion event?
Due April 19th, 2019 1. (3 pts) Consider two particles of mass mi and m2 (in one dimension) that interact via a potential that depends only on the dstance between the particles V(l 2), so that the Hamiltonian is Acting on a two-particle wave function the translation operator would be (a) Show that the translation operator can be written as where P- p p2 is the total momentum operator of the syste (b) Show that the total momentum is conserved...
1) Consider a uniform system of extremely relativistic (i.e., &p=cp) Bose gas with N particles in three-dimensions. (a) Calculate the density of states using the formula D(e) - .86 - c). (b) Find the Bose-Einstein condensation temperature T.. (e) Find the fraction of condensed bosons No/N as a function of T/T. (d) Find the total energy (E) for T <T.
Problem (3) A particle of mass M is at rest in the laboratory when it decays into three identical particles, each of mass m. Two of the particles, labeled #1 and #2, have velocity magnitudes and perpendicular directions as shown, with e representing the speed of light. Please use conservation of relativistic momentum to compute the direction and speed, expressed in terms of c, of particle #3 with respect to the laboratory (a) (b) Please compute the ratio M/m.
Problem...
Mechanics.
3. A particle of mass m moves in one dimension, and has position r(t) at time t. The particle has potential energy V(x) and its relativistic Lagrangian is given by where mo is the rest mass of the particle and c is the speed of light (a) Writing qr and denoting by p its associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy mzc2 6 marks (b) Write...
What is the rest mass of a particle with a relativistic momentum of 5.32 x 10^-19 kg*m/s and is moving at 0.75 c (c is the speed of light)?
3. Consider an ideal gas of N particles, each of mass M, confined to a one- dimensional line of length a. Find the entropy at temperature T
3. Consider an ideal gas of N particles, each of mass M, confined to a one- dimensional line of length a. Find the entropy at temperature T
(80 pts) Entropy of the ideal gas: Consider a monatomic gas of identical non-interacting particles of mass m. The kinetic energy of each particle is given in terms of its momentum p by Ekinp2/(2m). For a given total energy U, volume V and total particle number N (with N » 1) calculate the entropy S(U, V,N)-klog Ω(U, V,N), where Ω(U, V,N) counts the number of different microscopic configurations for given N, U and V. To get a finite number for...
Pb2. Consider the case of a canonical ensemble of N gas particles confined to a t rectangular parallelepiped of lengths: a, b, and c. The energy, which is the translational kinetic energy, is given by: o a where h is the Planck's constant, m the mass of the particle, and nx, ny ,nz are integer numbers running from 1 to +oo, (a) Calculate the canonical partition function, qi, for one particle by considering an integral approach for the calculation of...