Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 52E
To determine

To Calculate:

The ratio of expectation values of radial energy to the rotational energy.

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The harmonic oscillator eigenfunction ₁(x) = = 4a³\1/4 e-ax²/2, where a = μω ħ (a) Find (x²) for an oscillator in this state, and express your result in terms of u, w, and ħ. 1 (b) In an eigenstate it is always true that (T) = (V) for a harmonic oscillator. If ↑ =-=-=-=A² 2μ 1 and ✩ = µw²x², find (p²) when the system is in the state 1₁ (x). (Note: You can use the result found in part (a), or compute it directly from the form of the operator p.) 2
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