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## Homework Statement

use the variational method to approximate the ground state energy of the particle in a one-dimentional box using the normalized trial wavefunction ∅(x)=Nx[itex]^{k}[/itex](a-x)[itex]^{k}[/itex] where k is the parameter. Demonstrate why we choose the positive number rather than the negative value. By what absolute percentage does your value differ from the true one, (.125h[itex]^{2}[/itex]/m[itex]_{e}[/itex]a^2? It is also stated that

[itex]\oint[/itex]psi*Hpsi dx=([itex]\bar{h}[/itex]/m[itex]_{e}[/itex]a[itex]^{2}[/itex])(4k[itex]^{2}[/itex]+k)/(2k-1).

## Homework Equations

I'm pretty sure you have to use this one [itex]\oint[/itex]psi*Hpsi dx/[itex]\oint[/itex]psi*psi dx

## The Attempt at a Solution

The first thing I tried to do is normalize the trial wavefunction which didn't get very far as I couldn't figure out how to do the integral. I also can't figure out to get either of the integrals to work because of the k powers. That is the main thing I'm blocked on. The only other thing I can think of is just to take an approximation of just the first two k values but the given integral with the incorporated hamiltonian has k included so it's wanting me to approx over all k. I need help getting to the next step. Thanks!