Analyze a quantum wire with a rectangular cross-section of dimensions Lx=Ly. Assume infinite potential well. Looking for the three lowest confinement energies.
Analyze a quantum wire with a rectangular cross-section of dimensions Lx=Ly. Assume infinite potential well. Looking...
4. (20 points) Infinite Wells in Three Dimensions a) Consider a three dimensional in- finite rectangular well for which L -L, Ly-2L, ald L2-3L. In terms of quantum numbers (e.g. nz, ny, and n.), M. L, and ћ. write down an expression for the energies of all quantum states. (b) Find the energies of the ground state and the first three lowest lying energies. As in part (b), for each energy level, give the quantum numbers n, ny, n and...
Ex 5 Assume that N turns of wire are tightly wound on a toroidal frame of a rectangular cross section with dimensions as shown in Figure. Then, assuming the permeability of the medium to be Ho, find the self-inductance of the toroidal coil. FIGURE 6-23 A closely wound toroidal coil Ex 5 Assume that N turns of wire are tightly wound on a toroidal frame of a rectangular cross section with dimensions as shown in Figure. Then, assuming the permeability...
(25 marks) The one-dimensional infinite potential well can be generalized to three dimensions. The allowed energies for a particle of mass \(m\) in a cubic box of side \(L\) are given by$$ E_{n_{p} n_{r, n_{i}}}=\frac{\pi^{2} \hbar^{2}}{2 m L^{2}}\left(n_{x}^{2}+n_{y}^{2}+n_{z}^{2}\right) \quad\left(n_{x}=1,2, \ldots ; n_{y}=1,2, \ldots ; n_{z}=1,2, \ldots\right) $$(a) If we put four electrons inside the box, what is the ground-state energy of the system? Here the ground-state energy is defined to be the minimum energy of the system of electrons. You...
Problem 1 (20pts). An infinite wire has the cross-section shown in the figure with J. = 3r (A), and ), = 1 (A). (assume free space) Find the magnetic field H (r)for ranges: a) r<a b) a<r<b c) r> H(r) +z JO
Problem 1 (20pts). An infinite wire has the cross-section shown in the figure with 11 = 3r (A), and J2 = 1 (A). (assume free space) Find the magnetic field Ħ(r)for ranges: a) r<a b) a<r<b c) r>b H(r) +Z 12 b
Quantum Mechanics Problem 1. (25) Consider an infinite potential well with the following shape: 0 a/4 3al4 a h2 where 4 Using the ground state wavefunction of the original infinite potential well as a trial function, 2πχ trial = 1-sin- find the approximation of the ground state energy for this system with the variational method. (Note, this question is simplified by considering the two components of the Hamiltonian, and V, on their own) b) If we had used the 1st...
A hollow tube with a rectangular cross-section has external dimensions of 0.5 in by 1 in and a wall thickness of 0.05 in. Assume that the material is brass, for which the conductivity is 1 = 1.5×107 S/m. A DC current of 200 A is flowing through the outer part of the tube. Part a Calculate the potential difference across an L = 1 m length of the tube in the z direction. Part b Calculate the potential difference across...
II- Given 2 brass specimens with initial dimensions as follows: Specimen #1: rectangular cross-section (12 x 20 mm) Specimen #2: circular cross-section (Ø = 15 mm) Both specimens were cold worked until the final cross-section area became 100 mm2. a) (6) Calculate the percentage of cold work for both specimens. b) (3) After cold work, both specimens were heated at different temperatures in order to reach full recrystallization in one hour. Which specimen will require lower heat treatment temperature? Explain...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
Chapter 06, Problem 6.50 A steel alloy specimen having a rectangular cross section of dimensions 19.0 mm x 3.2 mm (0.7480 in. x 0.1260 in.) has the stress-strain behavior shown in the Animated Figure. If this specimen is subjected to a tensile force of 100900 N (22680 lbf) then (a) Determine the amount of elastic strain induced. (b) Determine the amount of plastic strain induced. (c) If its original length is 400 mm, what will be its final length after...