Problem 1
A particle of mass m is in the ground state in the harmonic oscillator potential 1 V(x) = 1/2 kx² where k = 300eV/nm²
A small perturbation β*x^4 is added to this potential. Estimate the first-order change for the energy of the particle.
The particle's ground state energy is 6 eV if β=0. Find its ground state energy to 3 significant figures if β = 20eV/nm^4.