Quantum Harmonic Oscillators with Wave Functions Having a Fixed Logarithmic Derivative at the Equilibrium Position

摘要

The exact solution of the Schroedinger equation for the systems and the boundary condition stated in the title is constructed. The familiar cases of the ordinary harmonic oscillator and the half oscillator are immediately identified. The connection with the double oscillator is also established and is helpful to understand the energy spectrum of the latter. Similar connections can be used to study other partial oscillators. (Atomindex citation 13:700711)