(see Image) 7. (a) What is the energy distribution function n(E) and why is it useful in the context ofstatistical physics? Consider an ideal gas vs. a "free electron gas", and write the generalexpression for the energy distribution function n(E) for each case separately.(b) In class, we derived the density of states for a free electron gas (i.e. electrons in ametal) using the model of the 3D infinite potential well which gives energy levels as:,πηE= (n² + n² + n²)2mL²where L is the side length of a cubical "box". Now suppose instead that we considerphysical systems in which the electrons are confined to move in a 2D "sheet" of sidelength L (e.g. a relevant material system is graphene), which can have energy levels givenas:Eh²x²~ 2m² F² (m² + n²)where m* is an "effective mass". Derive the density of states for the 2D electron gas.

Answered: Image /qna-images/answer/896e9422-aa75-4780-857e-8d37afe9f7e8.jpg

Answered: 7. (a) What is the energy distribution…

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter6: Quantum Mechanics In One Dimension

Section: Chapter Questions

Problem 16P

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PROBLEM 2. Consider a spherical potential well of radius R and depth Uo, so that the potential is U(r) = -Uo at r R. Calculate the minimum value of Uc for which the well can trap a particle with l = 0. This means that SE at Uo > Uc has at least one bound ground state at l = 0 and E < 0. At Ug = Uc the bound state disappears.
1. (a) Is the de Bruijn graph for 10-ary words of length 1 (that is, k = 10 and 1 = 1) planar? Justify your answer. (b) What about the de Bruijn graph for k = 4, l = 1?
Q3.1 Please answer the following question throughly and detailed. Need to understand the concept.
Problem 1: Bosons, Fermions Consider a system of five particles, inside a container where the allowed energy levels are nondegenerate and evenly spaced. For instance, the particles could be trapped in a one-dimensional harmonic oscillator potential. In this problem you will consider the allowed states for this system, depending on whether particles are identical fermions, identical bosons, or distinguishable particles. a) Describe the ground state of this system, for each of these three cases. b) Suppose that the system has one unit of energy (above the ground state). Describe the allowed states of the system, for each of the three cases. How many possible system states are there in each case? c) Repeat part (b) for two units of energy and for three units of energy. d) Suppose that the temperate of this system is low, so that the total energy is low (though not necessarily zero). In what way will the behavior of the bosonic system differ from that of the system of distinguishable…
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Problem 1: This problem concerns a collection of N identical harmonic oscillators (perhaps an Einstein solid) at temperature T. The allowed energies of each oscillator are 0, hf, 2hf, and so on. a) Prove =1+x + x² + x³ + .... Ignore Schroeder's comment about proving 1-x the formula by long division. Prove it by first multiplying both sides of the equation by (1 – x), and then thinking about the right-hand side of the resulting expression. b) Evaluate the partition function for a single harmonic oscillator. Use the result of (a) to simplify your answer as much as possible. c) Use E = - дz to find an expression for the average energy of a single oscillator. z aB Simplify as much as possible. d) What is the total energy of the system of N oscillators at temperature T?
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The essence of the statement of the uniqueness theorem is that if we know the conditions the limit that needs to be met by the potential of the system, then we find the solution of the system , then that solution is the only solution that exists and is not other solutions may be found. If we know potential solutions of a system, can we determine the type of system that generate this potential? If so, prove the statement! If no, give an example of a case that breaks the statement!
Please help answer all questions (a) (b) and (c). This is a question on Solid State Physics
Solve the following.
PROBLEM 3. Using the variational method, calculate the ground state en- ergy Eo of a particle in the triangular potential: U(r) = 0 r 0. Use the trial function v(x) = Cx exp(-ar), where a is a variational parameter and C is a normalization constant to be found. Compare your result for Eo with the exact solution, Eo 1.856(h? F/m)/3.
Q3.1 Please answer part D throughly and detailed. Need to understand the concept.

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