Self-adjoint extension procedure for a singular oscillator

• URL: http://arxiv.org/abs/2406.12927v1
• Date: Fri, 14 Jun 2024 21:21:38 GMT
• Title: Self-adjoint extension procedure for a singular oscillator
• Abstract summary: It is shown that the self-adjoint extension violates the well-known property of equidistance of energy levels. The concept of quantum defect is generally introduced, and the wave function of the problem is written as a single function.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: For a singular oscillator, the Schrodinger equation is obtained an equation of eigenvalues, and the dependence of energy on the self-adjoint extension parameter is established. It is shown that the self-adjoint extension violates the well-known property of equidistance of energy levels for the oscillatory potential, well-known in quantum mechanics. The concept of quantum defect is generally introduced, and the wave function of the problem is written as a single function.

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