Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 1 / 34C / c / i / Solution

Define $|\pm {⟩}_1=(|0{⟩}_1\pm |1{⟩}_1)/\sqrt{2}$. Since $B_1+B_1^{†}$ is the Pauli $X$ operator on the first oscillator, the exact eigenvectors arewith energies

Solved by gpt-5.6-sol high.