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
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter10: Introduction To Quantum Mechanics
Section: Chapter Questions
Problem 10.26E: For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the...
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![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa57c965-3aa3-4002-99cf-f9c626427d79%2Fdb74436e-76e6-483b-b9b1-c8852a45f253%2Feiiopbe_processed.png&w=3840&q=75)
Transcribed Image Text: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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