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.
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter11: Quantum Mechanics: Model Systems And The Hydrogen Atom
Section: Chapter Questions
Problem 11.22E
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