You have a harmonic oscillator with an angular frequency (w) and length parameter (a). The normalised energy eigenfunctions of this oscillator are Øn(x) and the corresponding energy eigenvalues are En = (n+1/2)hw, where n=0,1,2... using the lowering and raising operators  and Â+ the operator p̂x can be expressed as: p̂x = ih/a√2 (Â+ - Â) Can you please find the expectation values <p̂x2> in the ground state and first excited state of the oscillator.
You have a harmonic oscillator with an angular frequency (w) and length parameter (a). The normalised energy eigenfunctions of this oscillator are Øn(x) and the corresponding energy eigenvalues are En = (n+1/2)hw, where n=0,1,2... using the lowering and raising operators  and Â+ the operator p̂x can be expressed as: p̂x = ih/a√2 (Â+ - Â) Can you please find the expectation values <p̂x2> in the ground state and first excited state of the oscillator.
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics
Section: Chapter Questions
Problem 7.36P
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You have a harmonic oscillator with an angular frequency (w) and length parameter (a).
The normalised energy eigenfunctions of this oscillator are Øn(x) and the corresponding energy eigenvalues are En = (n+1/2)hw, where n=0,1,2...
using the lowering and raising operators  and Â+ the operator p̂x can be expressed as:
p̂x = ih/a√2 (Â+ - Â)
Can you please find the expectation values <p̂x2> in the ground state and first excited state of the oscillator.
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