Abstract
We investigate the complete analytical solutions of quantum mechanical harmonic and isotonic oscillators formulated in the commutative ring of bicomplex numbers. We obtain the explicit closed form expressions for the excited eigenstates and corresponding energy eigenvalues associated with the harmonic and isotonic oscillator potentials by extending the formalism adopted in Banerjee (Ann Phys 377:493, 2017) recently to find the analytical closed form solutions for ground states.
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Communicated by Vladislav Kravchenko
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Banerjee, A. Bicomplex Harmonic and Isotonic Oscillators: The Excited States. Adv. Appl. Clifford Algebras 27, 2321–2332 (2017). https://doi.org/10.1007/s00006-017-0772-4
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DOI: https://doi.org/10.1007/s00006-017-0772-4