Ground State Wave Equation:(adsbygoogle = window.adsbygoogle || []).push({});

ψ_{0}=(a/∏)^{(1/4)}e^{(-ax2/2)}

Prove the Heisenberg Uncertainty principle ≥h(bar)/2 by way of expectation values.

First I found <x>=0 because it was an odd function

then I found <Px>=0 because it was an odd function

Then <x^{2}>=∫(a/∏)^{(1/2)}x^{2}e^{(-ax2)/2}dx=1/2a by way of even function integral table

The problem I am having difficulty on is finding <Px^{2}>

It involves taking the double derivative and then integrating using a table (for me). I need to go through all of the derivatives and integrals I believe in order to get things to cancel so that only h/2 will be left over but I keep getting 0 for <Px^{2}>

I have literally been trying to work this out for ≈4-5 hrs so any help anyone can offer would be extremely appreciated.

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# Prove Heisenberg Uncertainty Principle for Ground State Harmonic Oscillator

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