Exact intrinsic half angular momentum from the Schrödinger equation

Abstract

The presence of (exact) intrinsic half angular moment (IHAM) in the Schrödinger equation has been explicitly shown through the spherical coordinates $(r,\theta ,\varphi )$ following a self-adjoint transformation. The special self-adjoint equations (SSAEs) were obtained by this self-adjoint transformation on the usual wavefunction of $\Psi (r,\theta ,\varphi ) =\Upsilon (r,\theta ,\varphi ) J(r,\theta ,\varphi )^{-1/2}$, where $J(r,\theta ,\varphi )$ is the Jacobian of the spherical coordinates. The first derivative terms of these SSAEs were absent. We considered the Kepler problem as applied to the hydrogen atom as an example. These SSAEs can easily be interpreted in terms of (semi)classical physics, and besides, these equations have exhibited an IHAM even for the ground state, i.e., without any excitation. This IHAM can be considered as a zero-point angular momentum.