A. Khondker

The Imaginary Component of the Weak Momentum: Spectral Vanishing and Gauge Invariance

We establish a rigorous functional-analytic framework for the imaginary component $p_I$ of the complex weak momentum $p_Q = p_R + ip_I = \frac{\hbar}{i}\nabla\ln\psi$. For every wavefunction in the Sobolev space $H^1(\Omega)$, including those with nodal sets, we prove that the expectation value of $p_I$ vanishes identi...