The time-independant Schroedinger equation for the harmonicosscilator in one dim

Question

The time-independant Schroedinger equation for the harmonicosscilator in one dimension is: where m is the mass of the quantum particle, and is thenatural frequency of oscillation. These are fixedparameters. Verify by explicitdifferentiation that the ground statesolution for this potential can be written as the Gaussian: provided that you set You will end up with an equation that determines the energy Ein terms of m and . What is the resulting value of E? So I've taken the first and second derivatives of theGaussian, and my answers for those are: and Now when I punch that in to the schroedinger, my proff saysthe x's should all cancel out, but im not getting that. Is there aproblem with my derivatives? or am I just missing something reallyobvious? I know when you divide by (x) from the E side, itcancels out all me e^ factors, and I am left with: after factoring out . Any help would be awesome. Thank you in advance

Explanation / Answer

nevermind. figured ou tmy dumb mistake.

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