Write the normalized form of the ground state wavefunction of the harmonic oscillator in terms of the variable y and the parameter α. (a) Write the integral you would need to evaluate to find the mean displacement <y>, and then use a symmetry argument to explain why this integral is equal to 0. (b) Calculate <y2> (the necessary integral will be found in the Resource section). (c) Repeat the process for the first excited state.
Write the normalized form of the ground state wavefunction of the harmonic oscillator in terms of the variable y and the parameter α. (a) Write the integral you would need to evaluate to find the mean displacement <y>, and then use a symmetry argument to explain why this integral is equal to 0. (b) Calculate <y2> (the necessary integral will be found in the Resource section). (c) Repeat the process for the first excited state.
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter12: Atoms And Molecules
Section: Chapter Questions
Problem 12.50E
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Write the normalized form of the ground state wavefunction of the harmonic oscillator in terms of the variable y and the parameter α. (a) Write the integral you would need to evaluate to find the mean displacement <y>, and then use a symmetry argument to explain why this integral is equal to 0. (b) Calculate <y2> (the necessary integral will be found in the Resource section). (c) Repeat the process for the first excited state.
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