Chapter4problem

(Problem submitted by team 9, based on problem 7.11 of Griffiths)

(a) Using the wave function $\psi ={\begin{cases}A*cos({\frac {\pi *x}{a}})&{\frac {-a}{2}}<x<{\frac {a}{2}}\\0&otherwise\end{cases}}$

obtain a bound on the ground state energy of the one-dimensional harmonic oscillator. Compare $<H>_{min}$ with the exact energy. Note: This trial wave function has a discontinuous derivative at ${\frac {\pm a}{2}}$.

(b) Use $\Psi =B*sin({\frac {\pi *x}{a}})$ on the interval (-a,a) to obtain a bound on the first excited state. Compare to the exact answer.