The wavefunction of a particle confined to a 2 y,(x) = √²₁ (¹²) sin one-dimensional box has the form: for 0 < x < L Based on the operator definitions ♬ = x for position, p, = (ħ/i) d/dx for linear momentum, and E₂ = − (ħ²/2m) d²/dx² for kinetic energy, derive the expressions for expectation values (x), (p,), and (E₁).
The wavefunction of a particle confined to a 2 y,(x) = √²₁ (¹²) sin one-dimensional box has the form: for 0 < x < L Based on the operator definitions ♬ = x for position, p, = (ħ/i) d/dx for linear momentum, and E₂ = − (ħ²/2m) d²/dx² for kinetic energy, derive the expressions for expectation values (x), (p,), and (E₁).
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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Transcribed Image Text:The wavefunction of a particle confined to a
2
y,(x) = √²₁
(¹²)
sin
one-dimensional box has the form:
for 0 < x < L
Based on the operator definitions ♬ = x for position, p, = (ħ/i) d/dx for linear momentum, and
E₂ = − (ħ²/2m) d²/dx² for kinetic energy, derive the expressions for expectation values (x), (p,),
and (E₁).
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