LC oscillator Hamiltonian H = Q²/(2C) + Φ²/(2L) as diagonal bilinear form in (Φ, Q)

LC-oscillator Hamiltonian as diagonal bilinear form. Setup: parallel LC circuit with inductance L, capacitance C; the stored energy is H_LC = (1/2L)·Φ² + (1/2C)·Q². This is a positive-definite bilinear form in the phase-space coordinates…