TL;DR
This paper introduces an exact method for calculating eigenenergies and eigenfunctions of quantum spiked oscillators using asymptotic expansions of Wronskians, demonstrated on three classic examples.
Contribution
It presents a novel procedure leveraging asymptotic Wronskian expansions for solving spiked oscillators exactly, advancing quantum eigenproblem techniques.
Findings
Successfully applied to three examples of spiked oscillators
Provides explicit eigenenergies and eigenfunctions
Enhances analytical tools for quantum oscillator problems
Abstract
A procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented. The originality of the method lies in an adequate use of asymptotic expansions of Wronskians of algebraic solutions of the Schroedinger equation. The procedure is applied to three familiar examples of spiked oscillators.
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