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In practice, we can only find analytic solutions for a few problems in quantum mechanics. We can solve some one-dimensional rectangular potential problems, the Dirac \(\delta \) potential, the harmonic oscillator and the hydrogen atom problem. Maybe we could list a few more cases, but not too many. Obviously, we need numerical and approximation methods to explore the beauty and power of quantum mechanics.

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Approximation Methods for Time-Independent Problems

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  • 发表日期：

    2026年

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  • Zoltán Papp

摘要

In practice, we can only find analytic solutions for a few problems in quantum mechanics. We can solve some one-dimensional rectangular potential problems, the Dirac \(\delta \) potential, the harmonic oscillator and the hydrogen atom problem. Maybe we could list a few more cases, but not too many. Obviously, we need numerical and approximation methods to explore the beauty and power of quantum mechanics.