Quantum Hamiltonian and Spectrum of Schrödinger Equation with Companied Harmonic Oscillator Potential and its Inverse in Both Three Dimensional Non-commutative Real Space and Phase

In present search, we have studied the effect of the both non commutativity of three dimensional space and phase on the Schrödinger equation with companied Harmonic oscillator potential and it’s inverse, know by isotopic Harmonic oscillator plus inverse quadratic (h.p.i.) potential, we shown that the Hermitian NC Hamiltonian formed anisotropic operator and described many physics phenomena’s, we have also derived the exact degenerated spectrum for studied potential in the first order of two infinitesimal parameters and associated for noncommutative space and phase, respectively

New Relativistic Atomic Mass Spectra of Quark (u, d and s) for Extended Modified Cornell Potential in Nano and Plank’s Scales

A novel study for the exact solvability of relativistic quantum spectrum systems for extended Cornell potential is discussed used both Boopp’s shift method and standard perturbation theory in noncommutativity three dimensional real space (NC-3DS), furthermore the exact corrections for the spectrum of studied potential was depended on infinitesimal parameter ∅ and a new discreet quantum numbers and we have also found the corresponding noncommutative Hamiltonian

The Klein–Gordon Equation with Modified Coulomb Potential Plus Inverse-Square–Root Potential in Three-Dimensional Noncommutative Space

In present work, the three-dimensional modified Klein-Gordon equation (MKGE) is analytically solved under modified Coulomb potential plus inverse-square–root potential, in the symmetries of noncommutative quantum mechanics (NCQM), using the generalized Bopp’s shift method. The new energy shift (ground state, first excited state and excited state) is obtained via first order perturbation theory in the 3-dimensional noncommutative real space (NC: 3D-RS) symmetries instead of solving MKGE with the Weyl Moyal star product. It is found that the perturbative solutions of discrete spectrum for studied potential depended on the parabolic cylinder functions, the Gamma function, the discreet atomic quantum numbers  and the potential parameters (and), in addition to noncommutativity parameters (and)

Deformed Quantum Energy Spectra with Mixed Harmonic Potential for Nonrelativistic Schrödinger Equation

The paper describes the deformed Hamiltonian for Schrödinger equation with mixed harmonic potential known by sextic potential and the corresponding spectrum of energies which depended with 3-new quantum numbers (j = l ± 1/2, l) and s = 1/2 in the non-commutativity infinitesimal parameter θ

A New Look at a Nonrelativistic Shell Model: Study of the Mirror Nuclei 17O and 17F in the Symmetries of NCQM

In present work, the 3-dimensional modified Schrödinger equation is analytically solved for nuclei 17O and 17F, which can be modeled as a doubly magic isotope  and , with one additional nucleon (valence) in the  level under modified quadratic Hellmann potential in the symmetries of noncommutative quantum mechanics (NCQM), using the generalized Bopp’s shift method. The new energy eigenvalues and the corresponding modified Hamiltonian operator are calculated in the 3-dimensional noncommutative real space phase (NC: 3D-RSP) symmetries. It is found that the perturbative solutions of the discrete spectrum can be expressed by the Gamma function, the discreet subatomic quantum numbers  and the potential parameters ( ), in addition to the noncommutativity parameters ( and ). The total complete degeneracy of new energy levels of the modified quadratic Hellmann potential changed to become equals to the value  instead of the initial values  in ordinary QM. Our results are in good agreement with the already existing literature in NCQM.

A New Model for Describing Heavy-Light Mesons in The Extended Nonrelativistic Quark Model Under a New Modified Potential Containing Cornell, Gaussian And Inverse Square Terms in The Symmetries Of NCQM

In present work, the modified Schrödinger equation (MSE) is analytically solved for the Heavy-Light Mesons (HLM) under modified quark-antiquark potential containing modified Cornell, Gaussian and inverse square terms MCGISTs, in the symmetries of 3-dimensional noncommutative real space phase (NC: 3D-RSP), using the generalized Bopp’s shift method. The energy a spectrum of HLM has been investigated in the framework of extended nonrelativistic quark model ENRQM. Furthermore, the new energy eigenvalues and the corresponding Hamiltonian operator are calculated in (NC: 3D-RSP) symmetries. The masses of the scalar, vector, pseudoscalar, and pseudovector for (,,  and ) mesons have been calculated in (NC: 3D-RSP) and we have shown that the spin-orbital coupling  generated automatically. Moreover, using the perturbation approach, we found that the perturbative solutions of discrete spectrum can be expressed by the parabolic cylinder functions function, Gamma function, the discreet atomic quantum numbers  of the  state and (the spin independent and spin dependent) parameters (), in addition to noncommutativity parameters (and). As a special case this model has been applied to study the S- and P-wave states of,,  and mesons  in NCQM symmetries The total complete degeneracy of new energy levels of HLM was changed to become equals the new value instead  in ordinary quantum mechanics. Our obtained results are in good agreement with the already existing literatures in NCQM.&nbsp

A Recent Study of Quantum Atomic Spectrum of the Lowest Excitations for Schrödinger Equation with Typical Rational Spherical Potential at Planck's and Nanoscales

The exact global quantum atomic spectrum of lowest excitations states (fundamental and first excited states) for Hydrogen atom with typical rational spherical potential like singular one-fraction power (s.o.f.p.) potential were reported by using both Boopp's shift method and stationary perturbation theory, at Planck's and Nano scales, in both non commutative 2-dimensional space and phase. We have also found the deformed anisotropic Hamiltonian for studied potential

Any L-States Solutions of The Modified Schrodinger Equation with Generalized Hellmann–Kratzer Potential Model in The Symmetries of NRNCQM

In the present research paper, the approximate analytical solutions of the modified radial Schrodinger equation (MSE) have been obtained with a newly proposed potential called generalized Hellmann–Kratzer potential (GHKP) model by using the improved approximation scheme to the centrifugal term for any l-states. The potential is a superposition of the Hellmann–Kratzer potential model and new terms proportional with (1/ r3, 1/ r4,  exp (-ar)/r2 and exp (-ar)/r3), appears as a result of the effects of noncommutativity properties of space and phase on the Hellmann–Kratzer potential model. We applied the generalized Bopp’s shift method and standard perturbation theory, in the nonrelativistic noncommutative three-dimensional real space phase (NC: 3D-RSP) instead to solving MSE directly with star product. The bound state energy eigenvalues for the some diatomic molecules such as, N2, CO, NO and CH  and obtained in terms of the generalized the Gamma function, the discreet atomic quantum numbers ((j, n, l, s, and m)), two infinitesimal parameters(a, b) which are induced automatically by position-position and phase-phase noncommutativity properties, in addition to, the dimensional parameters (V1, V, a, re, De) of GHKP model. Furthermore, we have shown that the corresponding Hamiltonian operator in (NC: 3D-RSP) symmetries is the sum of the Hamiltonian operator of the HKP model and two operators, the first one is the modified spin-orbit interaction while the second is the modified Zeeman operator for the previous diatomic molecule

A Recent Study of Quantum Atomic Spectrum of the Lowest Excitations for Schrödinger Equation with Typical Rational Spherical Potential at Planck's and Nanoscales

The exact global quantum atomic spectrum of lowest excitations states (fundamental and first excited states) for Hydrogen atom with typical rational spherical potential like singular one-fraction power (s.o.f.p.) potential were reported by using both Boopp's shift method and stationary perturbation theory, at Planck's and Nano scales, in both non commutative 2-dimensional space and phase. We have also found the deformed anisotropic Hamiltonian for studied potential

Quantum Hamiltonian and Spectrum of Schrödinger Equation with Companied Harmonic Oscillator Potential and its Inverse in Both Three Dimensional Non-commutative Real Space and Phase

In present search, we have studied the effect of the both non commutativity of three dimensional space and phase on the Schrödinger equation with companied Harmonic oscillator potential and it’s inverse, know by isotopic Harmonic oscillator plus inverse quadratic (h.p.i.) potential, we shown that the Hermitian NC Hamiltonian formed anisotropic operator and described many physics phenomena’s, we have also derived the exact degenerated spectrum for studied potential in the first order of two infinitesimal parameters and associated for noncommutative space and phase, respectively