Question

In lab you create a system where the Hamiltonian can be written as ? = ?0 + ?,

where ?0 is the Simple Harmonic Oscillator Hamiltonian,,-h22md2dx2+12kx2 , and ? is an applied

perturbation given by, Dx⁴.

1. What is the first order correction to the energy ground state energy,

  Ψ0=mωℏπ14 e(-mωx22ℏ)

What is the first order correction to the first excited state energy,

Ψ1=mωℏπ142mωℏ xe-mωx22ℏ

2. For the Simple Harmonic Oscillator system, the fundamental frequency is the v=0 to v=1

transition. Based on the first order corrections to the energy for the v=0 and v=1 energy level, how

much does this transition energy change by?

Answer 1