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This problem illustrates the application of Linear Variational Theory. Consider a particle of mass m in-a-box of length 1 but with a potential energy inside of the box which slopes upwards. V(x) = b(x -) if 0

This problem illustrates the application of Linear Variational Theory. Consider a particle of mass m in-a-box of length 1 but with a potential energy inside of the box which slopes upwards. V(x) = b(x -) if 0

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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This problem illustrates the application of Linear Variational Theory. Consider a particle of mass m in-a-box of length 1 but with a potential energy inside of the box which slopes upwards. V(x) = b(x – ) if 0 < x < 1 V(x) = co otherwise b is a constant which we will take in units of the particle in a box energies: 11h?n? b = 2m We will use a set of two basis functions consisting of the n=1 and n=2 particle in a box eigenfunctions. a. Show that the elements of the Hamiltonian matrix H11 and H22 can be calculated from the usual particle in a box energies.
Transcribed Image Text:This problem illustrates the application of Linear Variational Theory. Consider a particle of mass m in-a-box of length 1 but with a potential energy inside of the box which slopes upwards. V(x) = b(x – ) if 0 < x < 1 V(x) = co otherwise b is a constant which we will take in units of the particle in a box energies: 11h?n? b = 2m We will use a set of two basis functions consisting of the n=1 and n=2 particle in a box eigenfunctions. a. Show that the elements of the Hamiltonian matrix H11 and H22 can be calculated from the usual particle in a box energies.
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