THE QUANTUM MOMENTONIC ENERGY THEOREM The Missing Variable in Quantum Energy Accounting
Abstract
The kinetic energy of every quantum system decomposes exactly into two terms: T_flow, the energy of net momentum flow, and T_org, the energy of momentum organization — the Quantum Momentonic Potential. This decomposition follows from the Madelung representation ψ = √ρ · exp(iS/ℏ), established in 1927. It is an exact identity, not an approximation. What is new is the recognition that T_org is the quantum analogue of the Momentonic Potential Energy developed in classical Momentodynamics, and that its separate tracking provides a unified accounting framework for six major quantum phenomena: zero-point energy, the Casimir effect, spontaneous emission, quantum tunneling, the Lamb shift, and the Aharonov-Bohm effect. Each involves a change in T_org that, when tracked explicitly, unifies their energetic interpretation. The paper demonstrates this through three canonical systems. In the quantum harmonic oscillator, the zero-point energy ½ℏω is shown to consist of ¼ℏω of pure T_org — the minimum Quantum Momentonic Potential, which is the Dynamic Ground State of the mode. In the particle in a box, 100% of the energy is T_org; the particle has energy because its probability distribution is organized, not because it moves. In the hydrogen atom, the 1s electron has 13.6 eV of kinetic energy with zero momentum flow; falling deeper into the Coulomb well increases T_org, not decreases it. The Quantum Momentonic Energy Theorem is stated: E_total = T_flow + T_org + ⟨V⟩. Each term must be…
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