Modern quantum theory began to emerge in the mid 1920s with the publication of a number of seemingly unrelated articles that approached microscopic systems from radically different points of view. The idea of de-Broglie that the motion of a particle such as an electron in an atom could be explained by associating a wave with the particle led Schrodinger to a wave formulation of quantum theory. The first article by Schrodinger on wave mechanics was published in 1926. The success of this theory in describing the spectra of hydrogen seemed to indicate that the electron should be treated as a wave rather than a particle. While the wave theory of Schrodinger was yet to appear, Heisenberg, Max Born, and Jordan proposed a new theory in 1925. This theory, called matrix mechanics, was the first complete theory presented to scientific community as a method for solving atomic problems. Instead of questioning the particle nature of the electron, they called into question the classical concept of measuring process. Because microscopic systems are comparable in size to the smallest means available for measuring them, Heisenberg argued that the measurement of one variable of a microscopic system disturbs the values of other variables of the system and leads to an inherent uncertainty in the results of the measurement. The mathematical formulation of this idea, which has come to be called the Heisenberg Uncertainty Principle, is central to the modern interpretation of quantum mechanics.[ref-src-MPSE p64]

Heisenberg Uncertainty Principle

The position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision.

 \Delta x \cdot \Delta p = \frac{h}{4\pi}

 \Delta E \cdot \Delta t = \frac{h}{4\pi}

This uncertainty arises from the wave properties inherent in the quantum mechanical description of nature. Even with perfect instruments and technique, the uncertainty is inherent in the nature of things.

As you proceed downward in size to atomic dimensions, it is no longer valid to consider a particle like a hard sphere, because the smaller the dimension, the more wave-like it becomes. It no longer makes sense to say that you have precisely determined both the position and momentum of such a particle. When you say that the electron acts as a wave, then the wave is the quantum mechanical wavefunction and it is therefore related to the probability of finding the electron at any point in space. A perfect sine-wave for the electron wave spreads that probability throughout all of space, and the "position" of the electron is completely uncertain.

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