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Popov, Dušan

doi:10.1023/a:1021128830290

Cited by 8 publications

(8 citation statements)

References 11 publications

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“…Here, we have A = D e r 2 e , B = D e r e and c = −2D e [9,28,29,57,[62][63][64][65][66][67][68][69][70]73,[78][79][80][81][82].…”

Section: The 3-dimensional Schrödinger Equation For the Pseudoharmonimentioning

confidence: 99%

“…The expectation values of r 2 and p 2 can be obtained by applying the HellmannFeynman theorem (HFT) [80][81][82][88][89][90][91][92][93][94][95][96][97][98][99][100][101][102][103][104]. This theorem states that, a non-degenerate eigenvalue of a hermitian operator in a parameter dependent eigensystem varies with respect to the parameter according to the formula…”

Section: 2mentioning

confidence: 99%

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Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

Oyewumi

Sen

2012

J Math Chem

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For arbitrary values n and quantum numbers, we present the solutions of the 3-dimensional Schrödinger wave equation with the pseudoharmonic potential via the SU (1, 1) Spectrum Generating Algebra (SGA) approach. The explicit bound state energies and eigenfunctions are obtained. The matrix elements r 2 and r d dr are obtained (in a closed form) directly from the creation and annihilation operators. In addition, by applying the Hellmann-Feynman theorem, the expectation values of r 2 and p 2 are obtained. The energy states, the expectation values of r 2 and p 2 and the Heisenberg uncertainty products (HUP) for set of diatomic molecules (CO, NO, O 2 , N 2 , CH, H 2 , ScH) for arbitrary values of n and quantum numbers are obtained. The results obtained are in excellent agreement with the available results in the literature. It is also shown that the HUP is obeyed for all diatomic molecules considered.

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“…Here, we have A = D e r 2 e , B = D e r e and c = −2D e [9,28,29,57,[62][63][64][65][66][67][68][69][70]73,[78][79][80][81][82].…”

Section: The 3-dimensional Schrödinger Equation For the Pseudoharmonimentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

Oyewumi

Sen

2012

J Math Chem

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“…It is pertinent to note that on extending the work of Popov [88], we can obtained the quantum mechanical average values of the energy, the kinetic energy and the momentumsquare (as above) for the case of the pseudoharmonic potential in an arbitrary number of dimensions. Popov [88] obtained the following relations for expectation values of the energy and the kinetic energy from which we can also deduce the expectation value of the momentum-square as follows:…”

Section: Calculation Of Some Useful Expectation Values and The Virialmentioning

confidence: 99%

“…Popov [88] obtained the following relations for expectation values of the energy and the kinetic energy from which we can also deduce the expectation value of the momentum-square as follows:…”

Section: Calculation Of Some Useful Expectation Values and The Virialmentioning

confidence: 99%

“…Sage and Goodisman [98] considered the improvement on the conventional presentation of molecular vibrations where the advantages of the pseudoharmonic potential and direct construction of potential energy curve were discussed. The creation and annihilation operators and the corresponding coherent state of the pseudoharmonic oscillator potential were obtained by [88]. Dong [30] discussed the realization of dynamic group structure for the pseudoharmonic oscillator potential.…”

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confidence: 99%

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Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions

2007

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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 , r 2 , T , V , H , p 2 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.

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Quantum information entropies for the $$\ell $$ ℓ -state Pöschl–Teller-type potential

2016

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In this study, we obtained the position-momentum uncertainties and some uncertainty relations for the Pöschl-Teller-type potential for any ℓ. The radial expectation values of r −2 , r 2 and p 2 are obtained from which the Heisenberg Uncertainty principle holds for the potential model under consideration. The Fisher information is then obtained and it is observed that the Fisher-information-based uncertainty relation and the Cramer-Rao inequality hold for this even power potential. Some numerical and graphical results are displayed.

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Untitled

Cited by 8 publications

References 11 publications

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

Exact solutions of the Schrödinger equation for the pseudoharmonic potential: an application to some diatomic molecules

Exactly Complete Solutions of the Pseudoharmonic Potential in N-Dimensions

Quantum information entropies for the $$\ell $$ ℓ -state Pöschl–Teller-type potential

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