巴格曼空间中的三维谐振子和实体谐波

European Journal of Physics Pub Date : 2024-07-10 DOI:10.1088/1361-6404/ad61d1

D. Sunko, J. Cioslowski

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引用次数: 0

摘要

三维谐波振荡器在巴格曼空间中求解。这种处理方法在教学上比标准处理方法更加透明，但代价是要在一维振荡器的背景下介绍巴格曼变换。标准固态谐波的推导同样只需极少的技术难度，相当于一个完整的自足式论述，适合量子力学或物理学数学方法的入门课程。它提供了一个早期接触小波的机会，在信号分析和量子光学中有着重要的当代应用。

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The three-dimensional harmonic oscillator and solid harmonics in Bargmann space

The three-dimensional harmonic oscillator is solved in Bargmann space. The treatment is pedagogically more transparent than the standard ones, at the price of introducing the Bargmann transform in the context of the one-dimensional oscillator. The standard solid harmonics are similarly derived with minimal technical eﬀort, amounting to a complete self-contained exposition suitable for introductory courses in quantum mechanics or mathematical methods of physics. It provides an early exposure to wavelets, with important contemporary applications in signal analysis and quantum optics.

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European Journal of Physics

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