Consider a system of ? point particles obeying quantum mechanics constrained to move in a two-dimensional...

Consider a system of ? point particles obeying quantum mechanics constrained to move in a two-dimensional plane (1 2-D ideal quantum gas) in a microcanonical ensemble. Find a formula for the entropy ? via Ω, the number of microstates with energy ≤ ? and show that it is an extensive property of the system.

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genius_generous answered 2 years ago

Consider a system of three non-interacting particles confined by a one-dimensional harmonic oscillator potential and in...

Consider a system of three non-interacting particles confined by a one-dimensional harmonic oscillator potential and in thermal equilibrium with a total energy of 7/2 ħw. (a) what are the possible occupation numbers for this system if the particles are bosons. (b) what is the most probable energy for a boson picked at random from this system.

Consider a particle which is constrained to move along the surface of the sphere of radius...

Consider a particle which is constrained to move along the surface of the sphere of radius 5, centered at the origin. (a) If we write r(t) for the motion, write down the condition ‘constrained to move along the surface of the sphere of radius 5 centered at the origin’ in terms of r(t). (Hint. For later use, try to get rid of square roots.) (b) Explain why, for such a motion, we must have r 0 (t) ⊥ r(t). (Hint....

Consider a particle that is free (U=0) to move in a two-dimensional space. Using polar coordinates...

Consider a particle that is free (U=0) to move in a two-dimensional space. Using polar coordinates as generalized coordinates, solve the differential equation for rho and demonstrate that the trajectory is a straight line.

A. Describe specifically two major differences between quantum mechanics and classical mechanics. B. How does the...

A. Describe specifically two major differences between quantum mechanics and classical mechanics. B. How does the correspondence principle link quantum mechanics and classical mechanics? C. Why is it still accurate to use classical mechanics for human size objects? That is, why are our wave like properties not observed?

Consider the earth moon system quantum mechanically! Treat the earth and moon as point masses. Write...

Consider the earth moon system quantum mechanically! Treat the earth and moon as point masses. Write down the potential energy function for the earth/moon. Compare it to the potential energy function for the hydrogen atom. What is the “Bohr” radius for the earth/moon system? Estimate the principle quantum number (n) of the earth/moon system.

Consider a system of two particles in the xy plane: m1 = 2.10 kg is at...

Consider a system of two particles in the xy plane: m1 = 2.10 kg is at the location [r with arrow] 1 = (1.00 [i] + 2.00 [j] ) m and has a velocity of (3.00 [i] + 0.500 [j] ) m/s; m2 = 3.15 kg is at [r with arrow] 2 = (−4.00 [i] − 3.00 [j] ) m and has velocity (3.00 [i] - 2.00 [j] ) m/s. (a) Plot these particles on a grid or graph paper....

In a system of three particles, each particle has three quantum states. The energies of these...

In a system of three particles, each particle has three quantum states. The energies of these situations are 0.3? and 5?, respectively. Write the partition functions of the particles that meet the following conditions. a) If the particles are distinguishable b) Particles comply with Bose-Enistein statistics c) If the particles match Fermi-Dirac statistics

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal....

Consider the one dimensional model of one-particle-in-a-box. Under what condition the two quantum levels are orthogonal. Namely, find the relation between m and n so that < m | n > = 0

Quantum Mechanics Determine the settlement approach (approximation) for the harmonic oscillator system due to the relativistic...

Quantum Mechanics Determine the settlement approach (approximation) for the harmonic oscillator system due to the relativistic term using the perturbation method in order 2 correction.

Consider an ideal quantum gas of Fermi particles at a temperature T, a) Write the probability...

Consider an ideal quantum gas of Fermi particles at a temperature T, a) Write the probability p(n) that there are n particles in a state of one particle given as a function of the average occupation number, <n>. b) Find the root of the fluctuation to the average square in the occupation number of a single-particle state as a function of the occupation number average <n>. Sketch the result

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