Inconsistency of Probability Density in Quantum Mechanics and Its Solution

¹ Laboratory of Theoretical Physics and Natural Phylosophy, Physics Departement, Faculty of Mathematics and Natural Sciences, Institut Teknologi Sepuluh Nopember

² Laboratory of Theoretical Physics and Natural Phylosophy, Physics Departement, Faculty of Mathematics and Natural Sciences, Institut Teknologi Sepuluh Nopember

³ Laboratory of Theoretical Physics and Natural Phylosophy, Physics Departement, Faculty of Mathematics and Natural Sciences, Institut Teknologi Sepuluh Nopember

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.

KeywordsSchrodinger EquationProbability DensityParticle Conservation

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Inconsistency of Probability Density in Quantum Mechanics and Its Solution

Abstract

References (13)