Consider a particle subjected to the potential of a truncated harmonic oscillator

V (x) = 0.5m₀²x² when x > 0, when x < 0.

V(x)={0.5m02x2whenx>0whenx<0

We would like to use the variational method to estimate the ground state energy

a) Explain why a trial wave function of the form (x) = xe^x, where is a variational parameter might be a good wave function to use.

b) Use the variational method to estimate the ground state energy and compare with the exact result of E₁ = 1.5 ₀