Higher-dimensional oscillations of quantum particles

A theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions, based on an extension of the Schr\"{o}dinger equation to include 4$^{th}$ and 5$^{th}$ spatial components [E. R. Hedin, Physics Essays \textbf{25}, 2 (2012)]. A higher-dimensional harmonic oscillator confining potential localizes particles into 3-d space (characterizing the ``brane tension'' which confines Standard Model particles to the sub-manifold). Several consistency checks of this model are: a match with the quantum phenomenon of ``\textit{zitterbewegung}''; the predicted intrinsic spin angular momentum is of order h/2$\pi $; the magnetic moment of the electron is determined (with a gyromagnetic ratio of 2); the nuclear force ``hard core'' radius is accurately predicted; the ratio of quark masses (of the up and down quarks) is found to be consistent with QCD theory; and possible explanations of the Planck mass and Planck length. An application of higher-dimensional particle effects to the astrophysics of stars shows that radical physical inconsistencies are not evident. Finally, this model suggests a possible explanation of dark matter as the fractional probability manifestations of a ladder of the higher-dimensional symmetric excited states of ordinary particles.