Effects of size on the spectrum and stability of a confined on-center Hydrogen atom

Morcillo-Arencibia, Milagros F.; Sarsa, A.; Alcaraz-Pelegrina, J. M.

doi:10.1088/1402-4896/ac9be6

Cited by 1 publication

(3 citation statements)

References 81 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Starting from the 1s energy level, in figure 2(B), we find that it is almost unaffected for planes separation with D > 10 a.u.. For D < 10 a.u., it starts to rise, reaching a positive energy at D ∼ 2.3768 a.u.. In this case, the electron is not delocalized as it remains in the state n 1 ¢ = along the ρ-direction and l 1 ¢ = in the z-direction [ground state, equation (11)]. From equation (11), one finds that at…”

Section: Energy Levelsmentioning

confidence: 99%

“…In this case, the electron is not delocalized as it remains in the state n 1 ¢ = along the ρ-direction and l 1 ¢ = in the z-direction [ground state, equation (11)]. From equation (11), one finds that at…”

Section: Energy Levelsmentioning

confidence: 99%

“…These conditions lead to important quantum effects as the size of the confinement is reduced, such that the influence of shape on quantum confinement matters as much as size [1]. The wealth of problems related to this phenomenon range from atoms and molecules confined within nanotubes, fullerene traps [2][3][4][5][6][7][8][9][10][11], zeolitic nano-channels [12,13] to the behavior of donor centers in quantum-well semiconductor structures [14][15][16][17][18][19][20]. For example, the understanding of hydrogen-like donor impurity states in low-dimensional semiconductor structures is of importance in quantum dots and quantum-well wires [15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Electronic energy levels and wave-functions evolution from 3-D to 2-D of a hydrogen atom confined by two parallel planes

Cabrera-Trujillo

2024

Phys. Scr.

View full text Add to dashboard Cite

The compression of an atom produced by two planes induces a change in its electronic structure that evolves from a free atom in 3-D to a 2-D atom. This behavior is of importance in low-dimensional materials and high compression produced by an anvil cell. In this work, we study the evolution of the energy levels and electronic wave-functions of a hydrogen atom placed between two impenetrable planes as a function of the inter-plane separation through a numerical approach. As the inter-plane separation is reduced, the electron motion is restricted along the direction normal to the planes, similar to a particle in a box, while leaving the electron to move unrestricted along the planes, thus, breaking the spherical geometry of the H atom caused by the planes’ compression. The energy levels evolve from 3-D, described by nlm quantum numbers to a 2-D described by n′ml′, where l′ is the quantum number for a particle in a box along the z direction and n′ is the principal quantum number of the 2-D atom radial direction. We evaluate the energy levels from 3-D to 2-D and the radial average distance ⟨ρ⟩ in cylindrical coordinates, as a function of the inter-plane separation D along the z-direction. We find that as the inter-plane separation is reduced, the angular momentum quantum number l merges to the z-component of the angular momentum and it produces two branches, a symmetric for l-even and one anti-symmetric for l-odd, connected to a particle in a box quantum number l′ along the z-axis with implications in the atom photo-luminescence, resulting from the symmetry of the system. Furthermore, states with l-odd merge with states with l-even, as they have the same energy and average distance when D → 0. We provide an Aufbau principle for it. Our results agree to the analytical solutions at the 3-D and 2-D limiting cases.

show abstract

Section: Energy Levelsmentioning

confidence: 99%

Section: Energy Levelsmentioning

confidence: 99%