Linearity, Symmetry, and Prediction in the Hydrogen Atom

I.A. Malkin, Vladimir I. Man’ko

Oinam Babynanda Devi, C Amuba Singh

By invoking a standard variable transformation x → y ≡ x 2 that connects the eigenvalue problems of the hydrogen atom system (Coulomb potential) and the Kratzer oscillator system , we obtain a system of ladder operators Ω nl ± ( l = 0,1,2, ... , n − 1) that connect the degenerate energy eigenstates (belonging to different l -values) of the hydrogen atom system. Using such quantum number specific operators as the precursors, we develop a general method of constructing quantum number independent ladder operators ; and then investigate the general conditions for these operators to form a realization of the su (2) algebra. In the process, we demonstrate that, in general, a finite-dimensional linear vector space carries a realization of the su (2) algebra. Applying the method to the case at hand, we show that for the hydrogen atom system the operators and form an su (2) algebra. The Hamiltonian is identified with the Casimir operator of the algebra, thereby revealing a dynamical SU (2) group symmetry of the hydrogen atom system.

Keshav Narain Shrivastava

The probability of sticking of spin-polarised atomic hydrogen, H down arrow , on the superfluid helium surface as a function of temperature from 73 to 526 mK has been identified to arise from its interaction with third-sound ripplons. When the number density of the spin-polarised hydrogen atoms in the bulk helium becomes equal to that of the third-sound ripplons, the rate of sticking of H down arrow on the surface of the superfluid helium becomes a linear function of temperature. The predicted linearity is in accord with the experimental measurements.

Peter J. Mohr

V. Fock

Wolfgang Harbich, R. Hippler, Hans Kleinpoppen +1 more

The linear Stark effect of hydrogen was investigated for the metastable H(2s) state measuring the degree of linear polarization of field-induced Lyman-\ensuremath{\alpha} radiation. For sufficiently large electric fields (few kV/cm) the measured degree of linear polarization P is almost complete (P\ensuremath{\approxeq}-100%). This result is in excellent agreement with theoretical predictions, if the fine structure of hydrogen is taken into account.