Consider a 1D particle in a box confined between a = 0 and x = 3. The Hamiltonian for the particle inside thebox is simply given by Ĥ. Consider the following normalized wavefunction2m dz²¥(2) =35(x³ – 9x). Find the expectation value for the energy of the particle inside the box. Give your5832final answer for the expectation value in units of (NOTE: h, not hbar!). In your work, compare the expectationvalue to the lowest energy state of the 1D particle in a box and comment on how the expectation value youcalculated for the wavefunction ¥(x) is an example of the variational principle.

Answered: Image /qna-images/answer/bfd3facf-dce7-4527-8ba8-a52a0da74a92.jpg

Consider a 1D particle in a box confined between z = 0 and z = 3. The Hamiltonian for the particle inside the box is simply given by Ĥ *4 Consider the following normalized wavefunction 2m dr²° ¥(x) = / (x³ – 9x). Find the expectation value for the energy of the particle inside the box. Give your 35 3832 final answer for the expectation value in units of (NOTE: h, not hbar!). In your work, compare the expectation value to the lowest energy state of the 1D particle in a box and comment on how the expectation value you calculated for the wavefunction ¥(x) is an example of the variational principle.

Consider a 1D particle in a box confined between z = 0 and z = 3. The Hamiltonian for the particle inside the box is simply given by Ĥ *4 Consider the following normalized wavefunction 2m dr²° ¥(x) = / (x³ – 9x). Find the expectation value for the energy of the particle inside the box. Give your 35 3832 final answer for the expectation value in units of (NOTE: h, not hbar!). In your work, compare the expectation value to the lowest energy state of the 1D particle in a box and comment on how the expectation value you calculated for the wavefunction ¥(x) is an example of the variational principle.

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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