(a) Use a trial wave function of the form

to obtain a bound on the ground state energy of the one-dimensional harmonic oscillator. What is the “best” value of a? Compare (H)_min with the exact energy. Note: This trial function has a “kink” in it (a discontinuous derivative) at ±a/2; do you need to take account of this, as I did in Example 8.3?
(b) Use Ψ(x) = B Sin (πx/a) on the interval (-a,a) to obtain a bound on the first excited state. Compare the exact answer.

Transcribed Image Text:

(x): = 1 cos (x/a), -a/2