Problem 1: Two-level system. Canonical ensemble.Consider N impurity atoms trapped in a solid matrix.Each impurity can be in one of two states, with energies 0 and ɛ, respectively.The energy level are non-degenerate.1) Compute the partition function Z, for one subsystem (i.e. one impurity atom).2) Compute the partition function Z for the system.3) Deduce the free energy.4) Deduce the entropy.5) Deduce the internal energy.Problem 2: Two-level system. Canonical ensemble.Redo the above problem. We assume that the ground level is non degenerateand the excited level is g-fold degenerate.

Answered: Image /qna-images/answer/c975bce7-c57b-48bb-b770-547009cf59b8.jpg

Answered: Problem 1: Two-level system. Canonical…

Similar questions

1. Given the following probability density function: p(x) = Ae¬^(x-a)². 2. A particle of mass, m, has the wavefunction given by: Þ(x,t) = Ce-a[(mx²/h) + it] . 3. In a few sentences, explain why it is impossible to calculate (p) in the first problem, whereas in the second problem this is straightforward. Highlight the key concepts that differentiate these problems.
Q3/1 Find the difference State in Second and first excited energies (AE) of Particle 1-D with length (L).
B3
3. A system of N harmonic oscillators of frequency w are prepared in identical initial states of wavefunction Þ(x,0). It is found that the measurement of the energy of the system at t = 0 gives 0.5hw with probability 0.25, 1.5hw with probability 0.5 and 2.5hw with probability 0.25. a. Write a possible function p(x, 0). b. Write the corresponding (x, t). c. What is the expectation value of the Hamiltonian in the state p(x,t) ? d. Calculate the expectation value of position at time t
Q.3 What is zero-point energy? If a classical oscillator has energy 1/2 ℏ w, what is its amplitude?
1. A symmetric infinite well has the potential energy V(x) = { |x| a a. Write the corresponding Schrodinger equation and its solutions b. Write the boundary conditions c. Obtain the eigenfunctions and eigenvalues
Book: Classical Dynamics of Particles and Systems Topic: Calculus of Variations Please answer in a detailed solution. For study purposes. Thanks.
1. The Hamiltonian of the qubit in the standard basis is given by H = X⁰⁰ - X¹1 - ¡Xº¹ + ix¹⁰ (in units of eV). Find the possible values of the qubit energy E, and E₁ (in eV). Give the answer in decimals with accuracy to 3 significant figures.
ll Jazz LTE 2:48 PM @ 76% ( Classical-Dynamics-of-Particles-and-... PROBLEMS 97 245. Describe how to determine whether an equilibrium is stable or unstable when (d²U/dx²), = 0. 246. Write the criteria for determining whether an equilibrium is stable or unstable when all derivatives up through order n, (d"U/dx"), = 0. 247. Consider a particle moving in the region x>0 under the influence of the potential U(x) = Up where U, = 1 J and a = 2 m. Plot the potential, find the equilibrium points, and determine whether they are maxima or minima. 248. Two gravitationally bound stars with equal masses m, separated by a distance d, re- volve about their center of mass in circular orbits. Show that the period 7 is propor- tional to d/2 (Kepler's Third Law) and find the proportionality constant. 2-49. Two gravitationally bound stars with unequal masses m, and mg, separated by a dis- tance d, revolve about their center of mass in circular orbits. Show that the period 7 is proportional to d³/²…
B4
0 A physical system is described by a two-dimensional vector space with Hamiltonian operator Ĥ given by Ĥ = (_) where a is a constant. At time t = 0, the system is prepared in state (t = 0)) = -i2.5 0 determine the expectation value (Ŝ) at time t = πħ/(4x). O a. 2.17 O b. -2.50 O c. -1.25 O d. 2.50 O e. 5.00 0 (¹). For operator $ = (2 i2.5