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A concise general formula of the radial matrix element of the three-dimensional isotropic oscillator is derived using the properties of the general Laguerre polynomials. Some important special cases, such as the average value of the integer power of radial vector, the matrix element of the electric dipole transition and the element of the electric quadrupole transition, are obtained from the general formula.
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Keywords:
- three-dimensional isotropic oscillator /
- radial matrix element /
- general Laguerre polynomials /
- dipole transition /
- quadrupole transition
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