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## Homework Statement

Consider a particle in a box in the interval [-a,a]. Use the trial wavefunction

ψ

_{T}= x(a-x

^{2})

to obtain an approximate energy for the first excited state of the box as a function of a.

## Homework Equations

Schrodinger equation, Hamiltonian for atomic units is 1/2(d

^{2}/dx

^{2})

Normalized energy E = ∫

_{-a}

^{a}ψ*Hψdx/∫

_{-a}

^{a}ψ*ψdx

## The Attempt at a Solution

Right, so I just plugged in ψ

_{T}to the energy equation, and after evaluating the integrals, got E = 1-(3/5)a

^{2}/ [a(a

^{2}/7-1/15)]. The problem is, this function is discontinuous. It is discontinuous at 0, which makes sense to me, and at a = √(7/15), which I don't understand. I'm pretty sure my integrations were done properly... can anyone either explain this discontinuity to me, or tell me why my set-up was flawed?

Thanks!