Extensive Wave Function Question

arp777
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Homework Statement


A particle of mass 'm' moves in a 1-dimensional harmonic oscillator potential. The particle is in the first excited state. Calculate < x >, < x^2 >, < p >, and < p^2 >.


Homework Equations



Harmonic oscillating potential ---> V = (1/2) K x^2

First excited state (n=2)

Schrodinger's Equation


The Attempt at a Solution



I will be alright once I figure out the correct wave function to apply to this scenario. We have a massive particle in a harmonic oscillating potential. This potential is independent of time. Do I simply use a "guess Solution" at ψ(x,t) and have indeterminable constants carried with me throughout this problem? Or is there a way to find a more precise wave function just from the potential that can be used for calculating average position, average momentum, etc..? I have all relevant materials and quantum mechanics text in front of me. Just need some extra light.

Thanks so much!
 
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Haven't you already solved the Schrodinger equation for the simple harmonic oscillator? That's normally covered in a QM course.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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