Strongly perturbed harmonic oscillator

The limits of current micro-scale technology is approaching rapidly. As the technology is going toward nano-scale devices, physical phenomena involved are fundamentally different from micro-scale ones [1], [2]. Principles in classical physics are no longer powerful enough to explicate the phenomena involved in nano-scale devices. At this stage, quantum mechanic sheds some light on those topics which cannot be described by classical physics. The primary focus of this research work is the development of an analysis technique for understanding the behavior of strongly perturbed harmonic oscillators. Developing ``auxiliary' boundary value problems we solve monomially perturbed harmonic oscillators. Thereby, we assume monomial terms of arbitrary degree and any finite coefficient desired. The corresponding eigenvalues and eigenvectors can be utilized to solve more complex anharmonic oscillators with non polynomial anharmonicity or numerically defined anharmonicity. A large number of numerical calculations demonstrate the robustness and feasibility of our technique. Particular attention has been paid to the details as have implemented the underlying formula. We have developed iterative expressions for the involved integrals and the introduced ``Universal Functions.' The latter are applications and adaptations of a concept which was developed in 1990's to accelerate computations in the Boundary Element Method. <br>