Inconsistency of Probability Density in Quantum Mechanics and Its Solution

Agus Purwanto, Eny Latifah, Bintoro Anang Subagyo

Laboratory of Theoretical Physics and Natural Phylosophy, Physics Departement, Faculty of Mathematics and Natural Sciences, Institut Teknologi Sepuluh Nopember.

DOI: 10.4236/ojm.2012.22002                

Abstract

Probability density and particle conservation in quantum mechanics are discussed. The probability density has inconsistency with particle conservation in any quantum system. The inconsistency can be avoided by maintaining conservation of particle. The conservation coerces, a system should exist in a linear combinations of some eigenstates except ground state. The point is applied to the three exactly solvable quantum systems i.e. a particle in one dimensional well potential, harmonic oscillator and hydrogen atom.

Keywords

Schrodinger Equation; Probability Density; Particle Conservation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	R. P. Feynman, “Simulating Physics with Computers,” International Journal of Theoretical Physics, Vol. 21, No. 6-7, 1982, pp. 467-489. doi:10.1007/BF02650179
[2]	C. H. Bennett, et al., “Exprimental Quantum Cryptography,” Journal of Cryptology, Vol. 5, No. 1, 1992, pp. 3- 28. doi:10.1007/BF00191318
[3]	C. H. Bennett, et al., “Teleporting an Unknown Quantum State via Dual Classical and EPR Channels,” Physical Review Letters, Vol. 70, No. 13, 1993, pp. 1895-1899. doi:10.1103/PhysRevLett.70.1895
[4]	G. Auletta, “Foundations and Interpretation of Quantum Mechanics,” World Scientific, Singapore, 2001.
[5]	S. Gasiorowiczs, “Quantum Physics,” 3rd Edition, John Wiley & Sons Ltd., New York, 2003.
[6]	W. Greiner, “Quantum Mechanics, an Introduction,” 4th Edition, Springer, Berlin, 2001.
[7]	L. I. Schiff, “Quantum Mechanics,” McGraw-Hill, New York, 1949.
[8]	E. Merzbacher, “Quantum Mechanics”, 2nd Edition, John Wiley and Sons Ltd., New York, 1970.
[9]	D. J. Griffiths, “Introduction to Quantum Mechanics,” Prentice Hall, Upper Saddle River, 1995.
[10]	W. Heisenberg, “Uber Quantentheoretische Umdeutung Kinematischer und Nechanischer Beziehungen”, Zeischrift für Physik, Vol. 33, No. 1, 1925, pp. 879-893. doi:10.1007/BF01328377
[11]	E. Schrodinger, “Quantisierung als Eigenwertproblem. I and II,” Annalen der Physik, Vol. 79, 1926, pp. 361-376, 489-527.
[12]	E. Schrodinger, “Quantisierung als Eigenwertproblem. III,” Annalen der Physik, Vol. 80, 1926, pp. 437-490.
[13]	E. Schrodinger, “Quantisierung als Eigenwertproblem. IV,” Annalen der Physik, Vol. 81, 1926, pp. 109-139.