A new method to solve stationary one-dimensional Schroedinger equation is investigated. Solutions are described by means of representation of circles with multiple winding number. The results are demonstrated using the well-known analytical solutions of the Schroedinger equation.
The idea presented here of a general quantization rule for bound states is mainly based on the Riccati equation which is a result of the transformed, time-independent, one-dimensional Schrödinger equation. The condition imposed on the logarithmic derivative of the ground state function W0 allows to present the Riccati equation as the unit circle equation with winding number equal to one which, by...
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