Potential Energy and the Hydrogen Atom

Peter Woit

Guruh Sukarno Putra, Hamdi Akhsan

The energy for each level of the hydrogen atom was triggered by Neils Bohr, where the amount of energy decreases at every level of orbit. The value of energy depends on the principal quantum number which only applies to atoms with the s subshell of an atom with the same characteristics as the hydrogen atom. With the advancement of science, specifically in quantum physics, many potential equations aimed to solve the time-independent Schrodinger equation with the solution of the estimated value of energy. One of the applicable potential equations is the Hulthen potential which is explained about the potential at a small distance and only applies to atoms and micro-scale objects in physics and only has a solution at the azimuth quantum number value l = 0 or groups of atoms subshell s. Using the confluent hypergeometric function, the combination of the Hulthén potential and time-independent Schrödinger equation generates the estimated energy value of the hydrogen atom level, which can be used as a comparison with the estimated energy value of Bohr’s hydrogen atom. This study found that the comparison between Hulthén and Bohr energy level lies in the same ratio 1:1

Randell L Mills

Dan S. Zimmerman

A study is made of the interaction between hydrogen atoms and the surface elementary excitations of superfluid "He. Calculations for the sticking probability and for the energy and effective mass of a hydrogen atom bound to the surface are presented. As a first step in the calculations, we formulate the Hamiltonian describing a hydrogen atom interacting with the surface of "He in its ground state together with the interaction coupling to the surface elementary excitations (the ripplons). The derivation is based on the association of the surface ground state with a flat surface and the excited states with a sinusoidally varying height of the surface. The interaction potential is derived by summing a *He-H atom-atom pair potential over helium atoms below the surface. The atom-atom pair potential is chosen so that the derived surface potential is a Morse potential with parameters which are fitted to the effective surface potential derived by Mantz and Edwards for a hydrogen atom interacting with N-1 helium atoms. The energy and angle dependent sticking probability, S(E,θ), and the thermally averaged sticking probability, S(T), are calculated. Results are compared with the experimental value of S(T), S(T)=0.035±0.005, measured for the temperature range 0.18<T<0.27K. The possibility that a hydrogen atom bound above the surface may exhibit polaronic behaviour is investigated. The energy of the hydrogen surface "polaron" and its effective mass are calculated using perturbation theory. The hydrogen atom is found to be weakly coupled to the surface elementary excitations, and therefore the polaronic effects are weak. The contribution to these results from virtual transition to free states is emphasized.

G. Kunstatter, Saurya Das

Waldemar Wolney Filho

The purpose of this work is to show the stability of the hydrogen atom with the use the Quantum Oscillatory Modulated Potential and the Heisenberg equations of motion, postulating that the electron in the hydrogen atom is behaving as a quantum harmonic oscillator. With the electron confined between two potential barriers, created by the new potential function, we are considering that at absolute temperature the power absorbed or emitted by the electron per unit of time can be used to determine the zero point energy of the oscillator. Assuming that electron is only exchanging energy with the nucleus of the atom we are making use of the operators of creation and annihilation of a photon to explain how the energy between the proton and the electron can be exchanged to keep the atom a stable system.