# EFunction and Energy of Infinite potential + Parabolic potential well

## Homework Statement

Find eigenfunctions and the energy spectrum of a particle (its mass is m) in the potential well given by
V (x) = { +Infinity ; x < 0
{ (kx^2)/2 ; x > 0

SEq.

## The Attempt at a Solution

I think this is a combination of an infinite potential well combined with a parabolic approximation of a harmonic oscillator potential? I'm not 100% certain, and either way, I've spent a good 5+ hours working on this and haven't come up with much... I've read through Chapter 2.3 in Griffith's 2nd edition on The Harmonic Oscillator, and of course over the Ch 2.2 Infinite Square Well... I'm pretty sure I'm right when I say that the boundary conditions at x=0 require only odd functions such that ψ(x) = 0, and that ψ(x) is continuous at all points. Also if you have Griffiths, page 46 in Ch 2.3 explains with the ladder operators how to attain the different allowed energy levels of harmonic oscillator. I'm thinking that since this is essentially half of the parabolic approximation, that everything from this section would make sense, so long as you treat only the right side.... That being said, I would greatly appreciate if somebody could give me a little more direction here, as I seem to be rather stuck....

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