Analytic correlated wave functions in momentum space of excited S -states of Helium like Ions

Using the momentum space representation, we study the (2 + 1)-dimensional Duffin-Kemmer-Petiau oscillator for spin 0 particle under a magnetic field in the presence of a minimal length in the noncommutative space. The explicit form of energy eigenvalues is found, and the wave functions and the corresponding probability density are reported in terms of the Jacobi polynomials. Additionally, we also discuss the special cases and depict the corresponding numerical results.

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Molecular orbitals in momentum space

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1965.0151 ◽

1965 ◽

Vol 286 (1406) ◽

pp. 376-389 ◽

Cited By ~ 89

Keyword(s):

Momentum Space ◽

Wave Functions ◽

Basis Set ◽

Equilibrium Distance ◽

Numerical Work ◽

Algebraic Expressions ◽

Unitary Transformations ◽

The Matrix ◽

Internuclear Distances ◽

Ground State Energies

The troublesome problem of developing cusps in ordinary molecular wave functions can be avoided by working with momentum-space wavefunctions for these have no cusps. The need for continuum wavefunctions can be eliminated if one works with a hydrogenic basis set in Fock’s projective momentmn space. This basis set is the set of R 4 spherical harmonics and as a consequence one may obtain, solely by the ordinary angular momentum calculus, algebraic expressions for all the integrals required in the solution of the momentum space Schrödinger equation. A number of these integrals and a number of R 4 transformation coefficients are tabulated. The method is then applied to several simple united-atom and l.c.a.o. wavefunctions for H + 2 and ground state energies and corrected wavefunctions are obtained. It is found in this numerical work that the method is most appropriate at internuclear distances somewhat less than the equilibrium distance. In Fock’s representation both l.c.a.o. and unitedatom approximations become exact as the internuclear distance approaches zero. The united-atom expansion can be viewed as an eigenvalue equation for the root-mean-square momentum, p 0 = √( — 2 E ). In the molecule, the matrix operator corresponding to p 0 is related to the operator for the united-atom by a sum of unitary transformations, one for each nucleus in the molecule.

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Variational energies for highly excited states of the helium atom

Canadian Journal of Chemistry ◽

10.1139/v78-147 ◽

1978 ◽

Vol 56 (6) ◽

pp. 884-889 ◽

Cited By ~ 1

Author(s):

Wai-Tak Ma ◽

Mary Kuriyan ◽

Huw O. Pritchard

Keyword(s):

Helium Atom ◽

Excited States ◽

Wave Functions ◽

Experimental Results ◽

New States ◽

Variational Wave Functions ◽

Variational Wave ◽

S States

The efficient correlated variational wave functions used previously to study the higher 1 sns states of helium have been extended to other states of the helium atom, 1 snp (n ≤ 23), 2pnp1P (n ≤ 25), and 2pnp3P (n ≤ 25); similar uncorrelated wave functions were used for 1snd (n ≤ 21), 2pnp1D (n ≤ 10), and 2pnp3D (n ≤ 10). Attempts to use the same techniques for the 2pnp1,3S states appear to converge variationally to the energies of the 2s21S and 2s3s3S states respectively. Comparison is made with experimental results where appropriate, and agreement is excellent except in the case of the 1snd states above n = 13.A search was made for excited states of H− in each of these configurations, but no new states were found.

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Некоммутативная задача Ландау о фазовом пространстве при наличии минимальной длины

Вестник КРАУНЦ. Физико-математические науки ◽

10.26117/2079-6641-2020-33-4-188-198 ◽

2020 ◽

pp. 188-198

Author(s):

F.A. Dossa ◽

J.T. Koumagnon ◽

J.V. Hounguevou ◽

G.Y.H. Avossevou

Keyword(s):

Electromagnetic Field ◽

Phase Space ◽

Momentum Space ◽

Hypergeometric Functions ◽

Heisenberg Algebra ◽

Minimal Length ◽

Wave Functions ◽

Energy Eigenvalues ◽

Uvarov Method

The deformed Landau problem under a electromagnetic field is studied, where the Heisenberg algebra is constructed in detail in non-commutative phase space in the presence of a minimal length. We show that, in the presence of a minimal length, the momentum space is more practical to solve any problem of eigenvalues. From the Nikiforov-Uvarov method, the energy eigenvalues are obtained and the corresponding wave functions are expressed in terms of hypergeometric functions. The fortuitous degeneration observed in the spectrum shows that the formulation of the minimal length complements that of the non-commutative phase space. Изучается деформированная задача Ландау в электромагнитном поле, в которой алгебра Гейзенберга подробно строится в некоммутативном фазовом пространстве при наличии минимальной длины. Мы показываем, что при наличии минимальной длины импульсное пространство более практично для решения любой проблемы собственных значений. С помощью метода Никифорова-Уварова получаются собственные значения энергии, а соответствующие волновые функции выражаются через гипергеометрические функции. Случайное вырождение, наблюдаемое в спектре, показывает, что формулировка минимальной длины дополняет формулировку некоммутативного фазового пространства.

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