SHO with a fixed boundary

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How to solve the time-independent Schrödinger equation with the following potential:

U(x)=x^2 for x>x0
U(x)=infinity for x<x0 ?
 

Discussion

To the right side of x0 it's just a harmonic oscillator potential (of which I presume you know the solutions). What's the wavefunction for x<x0? Then apply boundary conditions.
 

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