- #1
Sciencenerd3
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Ground State Wave Equation:
ψ0=(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 <x2>=∫(a/∏)(1/2)x2e(-ax2)/2dx=1/2a by way of even function integral table
The problem I am having difficulty on is finding <Px2>
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 <Px2>
I have literally been trying to work this out for ≈4-5 hrs so any help anyone can offer would be extremely appreciated.
ψ0=(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 <x2>=∫(a/∏)(1/2)x2e(-ax2)/2dx=1/2a by way of even function integral table
The problem I am having difficulty on is finding <Px2>
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 <Px2>
I have literally been trying to work this out for ≈4-5 hrs so any help anyone can offer would be extremely appreciated.