ℋ❙φ❭ = (ℋ𝓍𝓎 + ℋ𝓏)❙φ❭ = E❙φ❭.

ℋ𝓍𝓎 = (P²𝓍 + P²𝓎)/(2μ) + ½ μω² (X² + Y²).

ℋ𝓏 = P²𝓏/2μ.

❙φ❭ = ❙φ𝓏𝓎❭ ⛒ ❙φ𝓏❭.

ℋ𝓍𝓎❙φ❭ = E𝓍𝓎❙φ❭.

E = E𝓍𝓎 + E𝓏.

❬z❙φ𝓏❭ = (2πħ)⁻¹ exp(ιp𝓏z/ħ).

E𝓏 = p𝓏²/2μ where p𝓏 is an arbitrary real constant.

ℰ = ℰ𝓍𝓎 ⛒ ℰ𝓏.