Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions
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We present analytically the exact solutions of the Schrödinger equation in the N-dimensional spaces for the pseudoharmonic oscillator potential by means of the ansatz method. The energy eigenvalues of the bound states are easily calculated from this eigenfunction ansatz. The normalized wavefunctions are also obtained. A realization of the ladder operators for the wavefunctions is studied and we deduced that these operators satisfy the commutation relations of the generators of the dynamical group SU(1,1). Some expectation values for 〈r−2〉, 〈r2〉, 〈T〉, 〈V〉, 〈H〉, 〈p2〉 and the virial theorem for the pseudoharmonic oscillator potential in an arbitrary number of dimensions are obtained by means of the Hellmann–Feynman theorems. Each solution obtained is dimensions and parameters dependent.
KeywordsN-dimensions Pseudoharmonic oscillator potential Schrödinger equation Exact solutions Hyperspherical harmonics Wavefunction ansatz Ladder operators SU(1, 1) Expectation values Hellmann–Feynman theorems Virial theorems
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