Radial wave function of 2D and 3D quantum harmonic oscillator

Adam Badra Cahaya

Abstract


One dimensional quantum harmonic oscillator is well studied in elementary textbooks of quantum mechanics. The wave function of one-dimensional oscillator harmonic can be written in term of Hermite polynomial. Due to the symmetry of the spring energy, the wave functions of two-dimensional and three-dimensional harmonic oscillators can be written as products of the one-dimensional case. Because of that, the wave functions of two- and three-dimensional cases are focused on cartesian coordinates. In this article, we utilize polar and spherical coordinates to describe the wave function of two- and three-dimensional harmonic oscillators, respectively. The radial part of the wave functions can be written in term of associated Laguerre polynomials.

Keywords


associated Laguerre polynomials; quantum harmonic oscillator; radial wave function; two dimension quantum harmonic oscillator; three dimension quantum harmonic oscillator

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References


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DOI: https://doi.org/10.15408/fiziya.v5i2.26172 Abstract - 0 PDF - 0

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