Ground State Energy Density of the Quantum Harmonic Oscillator
Firmin J. Oliveira
Hilo, Hawaii, USA.
DOI: 10.4236/jhepgc.2019.53049   PDF    HTML     540 Downloads   1,265 Views   Citations


The total energy of the ground state of the quantum harmonic oscillator is obtained with minimal assumptions. The vacuum energy density of the universe is derived and a cutoff frequency is obtained for the upper bound of the quantum harmonic oscillator.

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Oliveira, F. (2019) Ground State Energy Density of the Quantum Harmonic Oscillator. Journal of High Energy Physics, Gravitation and Cosmology, 5, 935-940. doi: 10.4236/jhepgc.2019.53049.

Conflicts of Interest

The author declares no conflicts of interest regarding the publication of this paper.


[1] Oliveira, F.J. (2016) First Instance of Cosmic Time and the Vacuum Density. arXiv:genph/1608.06525v1
[2] Carmeli, M. (2002) Cosmological Special Relativity. 2nd Edition, World Scienti_c, Singapore.
[3] Einstein, A. (1905) Does the Inertia of a Body Depend on Its Energy Content? Annalen der Physik, 17, 891; English translation in: The Principle of Relativity. Dover, New York, 1923: 35.
[4] Planck, M. (1899) Naturlische Masseinheiten. Der Koniglich Preussischen Akademie Der Wissenschaften, 479-480.
[5] Hubble, E. (1929) A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae. Proceedings of the National Academy of Sciences of the United States of America, 15, 168-173.
[6] Bonvin, V., Courbin, F., Suyu, S.H., Marshall, P.J., Rusu, C.E., Sluse, D., Tewes, M., Wong, K.C., Collett, T., Fassnacht, C.D., Treu, T., Auger, M.W., Hilbert, S., Koopmans, L.V.E., Meylan, G., Rumbaugh, N., Sonnenfeld, A. and Spiniello, C. (2016) H0LiCOW|V. New COSMOGRAIL Time Delays of HE 0435-1223: H0 to 3.8% Precision from Strong Lensing in a Flat _CDM Model. Monthly Notices of the Royal Astronomical Society, 465, 4914-4930. arXiv:1607.01790
[7] Rugh, S.E. and Zinkernagel, H. (2002) The Quantum Vacuum and the Cosmological Constant Problem. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 33, 663-705. arXiv:hepth/0012253
[8] Marsh, G.E. (2007) The Vacuum and the Cosmological Constant Problem. arXiv:0711.0220
[9] Heisenberg, W. (1927) Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift f üur Physik, 43, 172-198.
[10] Sato, K. and Suzuki, H. (1967) Analysis of Neutrino Burst from the Supernova 1987A in the Large Magellanic Cloud. Physical Review Letters, 58, 2722.
[11] Lobashev, V.M., Aseev, V.N., Belesev, A.I., Berlev, A.I., Geraskin, E.V., Golubev, A.A., Kazachenko, O.V., Kuznetsov, Yu.E., Ostroumov, R.P., Rivkis, L.A., Stern, B.E., Titov, N.A., Zadoroghny, C.V. and Zakharov, Yu.I. (2001) Direct Search for Neutrino Mass and Anomaly in the Tritium Beta-Spectrum: Status of \Troitsk Neutrino Mass" Experiment. Nuclear Physics B, 91, 280-286.
[12] Goobar, A., Hannestad, S., M öortsell, E. and Tu, H. (2006) The Neutrino Mass Bound from WMAP 3 Year Data, the Baryon Acoustic Peak, the SNLS Supernovae and the Lyman-_ Forest. Journal of Cosmology and Astroparticle Physics, 6, 19. arXiv:astroph/0602155
[13] Planck Collaboration: Ade, P.A.R., Aghanim, N., Arnaud, M., et al. (2016) Planck 2015 Results XIII. Cosmological Parameters. Astronomy and Astrophysics, 594, A13. arXiv:astroph/1502.01589
[14] Fahr, H.J. (2006) Cosmological Consequences of Scale-Related Comoving Masses for Cosmic Pressure, Mass, and Vacuum Energy Density. Foundations of Physics Letters, 19, 423-440.
[15] Weinberg, S. (1989) The Cosmological Constant Problem. Reviews of Modern Physics, 61, 1-23.
[16] Maia, M.D., Capistrano, A.J.S. and Monte, E.M. (2009) The Nature of the Cosmological Constant Problem. International Journal of Modern Physics A, 24, 1545-1548. arXiv:grqc/0905.3655
[17] Riess, A.G., Filippenko, A.V., Challis, P., Clocchiatti, A., Diercks, A., Garnavich, P.M., Gilliland, R.L., Hogan, C.J., Jha, S., Kirshner, R.P., Leibundgut, B., Phillips, M.M., Reiss, D., Schmidt, B.P., Schommer, R.A., Smith, R.C., Spyromilio, J., Stubbs, C., Suntze_, N.B. and Tonry, J. (1998) Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant.The Astronomical Journal, 116, 1009-1038. arXiv:astroph/9805201
[18] Sidharth, B.G. (2006) A Note on the Cosmic Neutrino Background and the Cosmological Constant. Foundations of Physics Letters, 19, 757-759.
[19] Sidharth, B.G. (2013) A Model for Neutrinos. International Journal of Theoretical Physics, 52, 4412-4415. arXiv:genph/0904.3639

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