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Shouldn't the integrating factor be ##exp(\frac{m\omega x}{\hbar})##?

[tex]\frac{\partial <x|0>}{\partial x} + \frac{m\omega x}{\hbar} <x|0> = 0 [/tex]

This is in the form:

[tex]\frac{\partial y}{\partial x} + P_{(x)} y = Q_{(x)} [/tex]

Where I.F. is ##exp (\int (P_{(x)} dx)##

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# Ground state of harmonic oscillator

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