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.
Highlights
Quantum mechanics is one of the greatest scientific achievements in 20th century
The conservation coerces, a system should exist in a linear combinations of some eigenstates except ground state
There are many phenomena which reveal, on a macroscopic scale, the quantum behavior of nature. It is in this sense that it can be said that quantum mechanics is the basis of our present understanding of all natural phenomena
Summary
Quantum mechanics is one of the greatest scientific achievements in 20th century. In the present state of scientific knowledge, quantum mechanics plays a fundamental role in the description and understanding of natural phenomena. It was introduced by Boltzmann in order to control the behavior of a system with a very large number of particles. It was the missing concept in order to understand the thermodynamics of macroscopic bodies, but the structure of the physical laws remained still deterministic. Tion of probability was needed as a consequence of our lack of knowledge of the initial conditions of the system and our ability to solve an enormous number of coupled nonlinear differential equations If we were both infinitely able experimentalists and infinitely able mathematicians, probability would be useless in classical physics: it is only a tool which allows imperfect beings, with a bounded brain like us, to control the behavior of many particle systems.
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