With explanation 1. Estimate the classical velocity for the (a) first and (b) fifth energy levels of a free electron traveling inone dimension and confined to a region of length 10 nm. [Answer: (a) 36 km/s]

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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 10.92E

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Chemistry
(a) Consider a wavefunction of the form: =1+x-1
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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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1. Estimate the classical velocity for the (a) first and (b) fifth energy levels of a free electron traveling in one dimension and confined to a region of length 10 nm. [Answer: (a) 36 km/s]