Energy levels of atomic hydrogen in a closed box: A natural cutoff criterion of the electronic partition function

This study aims to determine the thermodynamic properties of the parastatistics system of order two. The thermodynamic properties to be searched include the Grand Canonical Partition Function (GCPF) Z, and the average number of particles N. These parastatistics systems is in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD) and Bose-Einstein (BE). Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple thermodynamic functions for parastatistics system of order two are derived. The recursion linkages are then used to calculate the thermodynamic functions of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. From these results we concluded that from the Grand Canonical Partition Function (GCPF), Z, the thermodynamics properties of parastatistics system of order two (paraboson and parafermion) can be derived and have similar shape with parastatistics system of order one (Boson and Fermion). The similarity of the graph shows similar thermodynamic properties. Keywords: parastatistics, thermodynamic properties

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Theory of the energy levels and precise two-photon spectroscopy of atomic hydrogen and deuterium

Journal of Physics B Atomic Molecular and Optical Physics ◽

10.1088/0953-4075/29/8/021 ◽

1996 ◽

Vol 29 (8) ◽

pp. 1573-1573 ◽

Cited By ~ 2

Author(s):

K Pachucki ◽

D Leibfried ◽

M Weitz ◽

A Huber ◽

W König ◽

...

Keyword(s):

Atomic Hydrogen ◽

Energy Levels ◽

Two Photon

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Perturbation Theory

Quantum Mechanics ◽

10.23943/princeton/9780691209821.003.0005 ◽

2019 ◽

pp. 259-322

Author(s):

P.J.E. Peebles

Keyword(s):

Perturbation Theory ◽

Atomic Hydrogen ◽

Energy Levels ◽

Time Variable ◽

Approximation Schemes ◽

Hyperfine Line ◽

Approximation Methods ◽

Theoretical Understanding ◽

Chapter Deal ◽

Electronic Computers

This chapter examines applications drawn from perturbation theory. The main topic in perturbation theory is the energy and spontaneous decay rate of the 21-cm hyperfine line in atomic hydrogen. Before there were electronic computers, people had quite an accurate theoretical understanding of the energy levels in helium and more complicated systems. The trick was (and is) to find approximation schemes that treat unimportant parts of a physical system in quite crude approximations while reducing the interesting parts to a problem simple enough that it is feasible to compute but yet detailed enough to yield accurate results. The approximation methods in the chapter deal with the effects of small changes in the Hamiltonian, resulting for example from the application of a static or time variable electric or magnetic field. This may cause small changes in energy levels, and it may induce transitions among eigenstates of the original Hamiltonian.

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