Magnetic Field Induction and Time Intervals of the Electron Transitions Approached in a Classical and Quantum-Mechanical Way

Author(s)
Stanisław Olszewski

ABSTRACT

The motion of electron wave packets of a metal is examined classically in the presence of the magnetic field with the aim to calculate the time intervals between two states lying on the same Fermi surface. A lower limiting value of the transition time equal to about 10–18 sec is estimated as an average for the case when the states are lying on the Fermi surface having a spherical shape. Simultaneously, an upper limit for the electron circular frequency in a metal has been also derived. A formal reference of the classical transition time to the time interval entering the energy-time uncertainty relations known in quantum mechanics is obtained.

The motion of electron wave packets of a metal is examined classically in the presence of the magnetic field with the aim to calculate the time intervals between two states lying on the same Fermi surface. A lower limiting value of the transition time equal to about 10–18 sec is estimated as an average for the case when the states are lying on the Fermi surface having a spherical shape. Simultaneously, an upper limit for the electron circular frequency in a metal has been also derived. A formal reference of the classical transition time to the time interval entering the energy-time uncertainty relations known in quantum mechanics is obtained.

KEYWORDS

Lorentz Force and Magnetic Induction, Electron Wave Packets, Changes of the Electron Momentum, Transition Time between Quantum States

Lorentz Force and Magnetic Induction, Electron Wave Packets, Changes of the Electron Momentum, Transition Time between Quantum States

Cite this paper

nullS. Olszewski, "Magnetic Field Induction and Time Intervals of the Electron Transitions Approached in a Classical and Quantum-Mechanical Way,"*Journal of Modern Physics*, Vol. 2 No. 11, 2011, pp. 1305-1309. doi: 10.4236/jmp.2011.211161.

nullS. Olszewski, "Magnetic Field Induction and Time Intervals of the Electron Transitions Approached in a Classical and Quantum-Mechanical Way,"

References

[1] B. d’Espagnat, “Veiled Reality: An Analysis of Present- Day Quantum Mechanical Concepts,” Westview Press, Boulder, Colorado 2003.

[2] R. J. Cook, “Physical Time and Physical Space in General Relativity,” American Journal of Physics, Vol. 72, 2004, pp. 214-219. doi:10.1119/1.1607338

[3] C. Kittel, “Quantum Theory of Solids,” 2nd Edition, Wiley, New York, 1987.

[4] C. Kittel, “Introduction to Solid State Physics,” 7th Edition, Wiley, New York 1996.

[5] S. S. De, A. K. Ghosh and M. Bera, “On some Physical Characteristics of Ga,As-(Ga,Al)As Quantum-Well Photoluminescence,” Canadian Journal of Physics, Vol. 76, No. 2, 1998, pp. 105-110. doi:10.1139/cjp-76-2-105

[6] S. T. Perez-Merchancano, M. de Dios-Leyva and L. E. Oliveira, “Photoluminescence under Quasistationary Excitation Conditionsin Quantum Wells and Quantum-Well Wires,” Journal of Luminescence, Special Issue: Proceedings of the International Conference on Luminescence and Optical Spectroscopy of Condensed Matter, Vol. 72-74, 1997, pp. 389-390.

[7] S. T. Perez-Merchancano, M. de Dios-Leyva and L. E. Oliveira, “Radiative Recombination in Cylindrical GaAs- (Ga,Al)As Quantum-Well Wires under Quasistationary Excitation Conditions,” The Physical Review B, Vol. 53, No. 19, 1996, pp. 12985-12989. doi:10.1103/PhysRevB.53.12985

[8] L. E. Oliveira and M. de Dios-Leyva, “Radiative Lifetimes, Quasi-Fermi-Levels and Carrier Densities in GaAs- (Ga,Al))As Quantum-Well Photoluminescence under Steady State Excitation Conditions,” The Physical Review B, Vol. 48, No. 20, 1993, pp. 15092-15102. doi:10.1103/PhysRevB.48.15092

[9] J. C. Slater, “Quantum Theory of Molecules and Solids,” Vol. 3, McGraw-Hill, New York, 1967.

[10] N. W. Ashcroft and N. D. Mermin, “Solid State Physics,” Holt, Rinehart and Winston, New York, 1976.

[11] L. I. Schiff, “Quantum Mechanics,” 3rd Edition, McGraw- Hill, New York, 1968.

[1] B. d’Espagnat, “Veiled Reality: An Analysis of Present- Day Quantum Mechanical Concepts,” Westview Press, Boulder, Colorado 2003.

[2] R. J. Cook, “Physical Time and Physical Space in General Relativity,” American Journal of Physics, Vol. 72, 2004, pp. 214-219. doi:10.1119/1.1607338

[3] C. Kittel, “Quantum Theory of Solids,” 2nd Edition, Wiley, New York, 1987.

[4] C. Kittel, “Introduction to Solid State Physics,” 7th Edition, Wiley, New York 1996.

[5] S. S. De, A. K. Ghosh and M. Bera, “On some Physical Characteristics of Ga,As-(Ga,Al)As Quantum-Well Photoluminescence,” Canadian Journal of Physics, Vol. 76, No. 2, 1998, pp. 105-110. doi:10.1139/cjp-76-2-105

[6] S. T. Perez-Merchancano, M. de Dios-Leyva and L. E. Oliveira, “Photoluminescence under Quasistationary Excitation Conditionsin Quantum Wells and Quantum-Well Wires,” Journal of Luminescence, Special Issue: Proceedings of the International Conference on Luminescence and Optical Spectroscopy of Condensed Matter, Vol. 72-74, 1997, pp. 389-390.

[7] S. T. Perez-Merchancano, M. de Dios-Leyva and L. E. Oliveira, “Radiative Recombination in Cylindrical GaAs- (Ga,Al)As Quantum-Well Wires under Quasistationary Excitation Conditions,” The Physical Review B, Vol. 53, No. 19, 1996, pp. 12985-12989. doi:10.1103/PhysRevB.53.12985

[8] L. E. Oliveira and M. de Dios-Leyva, “Radiative Lifetimes, Quasi-Fermi-Levels and Carrier Densities in GaAs- (Ga,Al))As Quantum-Well Photoluminescence under Steady State Excitation Conditions,” The Physical Review B, Vol. 48, No. 20, 1993, pp. 15092-15102. doi:10.1103/PhysRevB.48.15092

[9] J. C. Slater, “Quantum Theory of Molecules and Solids,” Vol. 3, McGraw-Hill, New York, 1967.

[10] N. W. Ashcroft and N. D. Mermin, “Solid State Physics,” Holt, Rinehart and Winston, New York, 1976.

[11] L. I. Schiff, “Quantum Mechanics,” 3rd Edition, McGraw- Hill, New York, 1968.