For a particle in one-dimensional box of length a, y, = ax(a – x) and yw2 = x(a – x)(a + x) can each be also as an approximate solutions. (i) How large is then the underestimation in ground state energy (in %) using these 1/2 Wi or w2 as compared to the exact solution using y = (2/a)"²sin(nax/a). (ii) Which of them (w, or w2) give a closer estimation of the energy? %3D

For a particle in one-dimensional box of length a, y, = ax(a – x) and yw2 = x(a – x)(a + x) can each be also as an approximate solutions. (i) How large is then the underestimation in ground state energy (in %) using these 1/2 Wi or w2 as compared to the exact solution using y = (2/a)"²sin(nax/a). (ii) Which of them (w, or w2) give a closer estimation of the energy? %3D

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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Question

For a particle in one-dimensional box of length a, w, = ax(a – x) and w2 = x(a – x)(a + x)
can each be also as an approximate solutions.
(i) How large is then the underestimation in ground state energy (in %) using these
1/2
W1 or wz as compared to the exact solution using w = (2/a)""sin(nnx/a).
(ii) Which of them (w, or w2) give a closer estimation of the energy?

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