WKB Energy Expression for the Radial Schrödinger Equation with a Generalized Pseudoharmonic Potential (original) (raw)
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Exact solution of Schrödinger equation for Pseudoharmonic potential
Journal of Mathematical Chemistry, 2008
Exact solution of Schrödinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The energy eigenvalues are calculated numerically for some values of ℓ and n with n ≤ 5 for some diatomic molecules.
Journal of Mathematical Chemistry, 2012
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.
On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz
Open Physics, 2008
Making an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrödinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, δ and ν are also given, where η depends on a linear combination of the angular momentum quantum number ℓ and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.
On the solutions of the Schrodinger equation with some molecular potentials: wave function ansatz
2007
Making an ansatz to the wave function, the exact solutions of the D -dimensional radial Schrodinger equation with some molecular potentials like pseudoharmonic and modified Kratzer potentials are obtained. The restriction on the parameters of the given potential, δ and η are also given, where η depends on a linear combination of the angular momentum quantum number ℓ and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D=3, we find that the bound state eigensolutions recover their standard analytical forms in literature.
2009
The Schrodinger equation for the rotational-vibrational (ro-vibrational) motion of a diatomic molecule with empirical potential functions is solved approximately by means of the Nikiforov-Uvarov method. The approximate ro-vibratinal energy spectra and the corresponding normalized total wavefunctions are calculated in closed form and expressed in terms of the hypergeometric functions or Jacobi polynomials P_n^(μ,ν)(x), where μ>-1, ν>-1 and x included in [-1,+1]. The s-waves analytic solution is obtained. The numerical energy eigenvalues for selected H_2 and Ar_2 molecules are also calculated and compared with the previous models and experiments.
Exact polynomial eigensolutions of the Schrödinger equation for the pseudoharmonic potential
Journal of Molecular Structure: THEOCHEM, 2007
The polynomial solution of the Schrödinger equation for the Pseudoharmonic potential is found for any arbitrary angular momentum l. The exact bound-state energy eigenvalues and the corresponding eigen functions are analytically calculated. The energy states for several diatomic molecular systems are calculated numerically for various principal and angular quantum numbers. By using a proper transformation, this problem can be also solved very simply using the known eigensolutions of anharmonic oscillator potential.
Exact solutions of the radial Schrödinger equation for some physical potentials
Open Physics, 2007
By using an ansatz for the eigenfunction, we have obtained the exact analytical solutions of the radial Schrödinger equation for the pseudoharmonic and the Kratzer potentials in two dimensions. The bound-state solutions are easily calculated from this eigenfunction ansatz. The corresponding normalized wavefunctions are also obtained.
Canadian Journal of Chemistry, 2020
The low- and high-lying rovibrational energy levels of the Schrodinger equation with the molecular Tietz–Hua potential are obtained via the Wentzel–Kramers–Brilluoin (WKB) quantization approach. The Pekeris-type approximation scheme is applied to deal with the orbital centrifugal term of the effective potential function. The obtained energy spectra and the rotational–vibrational (rovibrational) coefficients for [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] diatomic molecules were compared with the ones obtained by other analytical methods and available experimental data in the literature. The results revealed that the accuracy of the energy spectra for the high-lying rovibrational quantum states may depend on the rotational-vibrational constants.
Exact solution of Schrodinger equation for Pseudoharmonic potentia
arXiv (Cornell University), 2007
Exact solution of Schrodinger equation for the pseudoharmonic potential is obtained for an arbitrary angular momentum. The energy eigenvalues and corresponding eigenfunctions are calculated by Nikiforov-Uvarov method. Wavefunctions are expressed in terms of Jacobi polynomials. The energy eigenvalues are calculated numerically for some values of ell\ellell and n with n<5 for some diatomic molecules.