In this assignment we will are attempting to find an approximate solution to the ground state...
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In this assignment we will are attempting to find an approximate solution to the ground state energy of a particle constrained on the positive z-axis in the one- dimensional well (1) V(x) = We can use units h = m = 1 to simplify calculations. In these units the Hamiltonian is H -{-20 J-xe-/a, x>0 otherwise = 1 2 dr + V(x), x > 0. Question 1 Variational Method To start we will apply the variational theorem to obtain an approximate solution to the ground state energy (a) Sketch the potential, indicating the effect of a and X. Sketch the ground state wavefunction in the potential. (b) Use the variational method to estimate the ground state energy for X = 2 and a = 2. Consider any reasonable trial function you like, parameterised in as many variables a, 3,... as you like. Take (H) (26/26) and find the minimum energy with respect to your parameters (2) E = DE = ... = 0. 3 Your job is to get the lowest energy in the class. If you have difficulty, try using the trial function from the question below. In this assignment we will are attempting to find an approximate solution to the ground state energy of a particle constrained on the positive z-axis in the one- dimensional well (1) V(x) = We can use units h = m = 1 to simplify calculations. In these units the Hamiltonian is H -{-20 J-xe-/a, x>0 otherwise = 1 2 dr + V(x), x > 0. Question 1 Variational Method To start we will apply the variational theorem to obtain an approximate solution to the ground state energy (a) Sketch the potential, indicating the effect of a and X. Sketch the ground state wavefunction in the potential. (b) Use the variational method to estimate the ground state energy for X = 2 and a = 2. Consider any reasonable trial function you like, parameterised in as many variables a, 3,... as you like. Take (H) (26/26) and find the minimum energy with respect to your parameters (2) E = DE = ... = 0. 3 Your job is to get the lowest energy in the class. If you have difficulty, try using the trial function from the question below.
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Related Book For
Introduction To Quantum Mechanics
ISBN: 9781107189638
3rd Edition
Authors: David J. Griffiths, Darrell F. Schroeter
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