Quantum Mechanics: Bohr's Atomic Model and the Heisenberg Uncertainty Principle (Part 2/2)

Energy radiated by matter is emitted in discrete packets or quanta. With that realization Max Planck founded the complex field of quantum physics. It inspired many physicists at the start of the 20th century. One of them was Niels Bohr, whose atomic model helped to explain the chemical behavior of matter. That behavior is directly influenced by the number of electrons in the outermost shells of atoms. Only when the outer shell is “fully occupied” by electrons does a compound attain its greatest possible stability. Take when two hydrogen atoms and one oxygen atom combine to form the molecule water. The oxygen atom needs two more electrons to complete its outermost shell, while each of the hydrogen atoms has one to give up. When they come together, the three atoms “share” the eight outer electrons in a kind of electron cloud to achieve a stable state. In contrast, noble gases such as helium or neon are very non-reactive because their outer shells are already “fully occupied” by electrons. A look at the periodic table shows how Bohr’s ideas apply to the elements. They are arranged in groups according to their number of outer electrons. Further major discoveries in quantum mechanics followed during the 1920s. Using Bohr’s atomic model Louis de Broglie was able to show that not only do electromagnetic waves such as light have particle qualities but also that particles of matter such as electrons exhibit wave character. The first precise mathematical representation of quantum mechanics was created by Werner Heisenberg with the “matrix mechanics” he formulated in 1925. A year later Erwin Schrödinger developed the wave equation, an alternative mathematical formulation of quantum mechanics. He was also the one who came up with the famous cat paradox. And Paul Dirac was able to show that Heisenberg’s and Schrödinger’s formulations were equivalent. In 1933 Schrödinger and Dirac shared the Nobel Prize. One of the most important rules of quantum mechanics was introduced in 1927 by Werner Heisenberg. It says that on the atomic level certain pairs of physical properties, such as the momentum and position of an electron, cannot be simultaneously measured with precision. The more precisely the one quantity is determined, the more “uncertain” the other is. Why is that? Because all objects in the universe essentially have wave and particle properties. However, an elephant compared to an electron is too large for this effect to be apparent. For an electron Heisenberg’s uncertainty principle means that a microscopic determination of its position influences its momentum. And a further conclusion that can be drawn is that the observer interferes in the event. That is the same for Schrödinger’s cat-thought experiment. The observer can only know if the cat is dead or alive once the box is opened but that influences the system and a probability has suddenly turned into reality. Heisenberg’s work was awarded the Nobel Prize in 1932. The uncertainty principle is of fundamental importance in quantum mechanics. But it plays virtually no role in macroscopic systems. In general terms, physicists agree on what is known as the correspondence principle. When moving from micro to macro systems, the laws of quantum mechanics become those of classical physics. The discussion within the physics community about how to interpret quantum mechanics led to the so-called Copenhagen interpretation –matter at quantum dimensions has both particle and wave character. But these two pictures of reality are subject to fundamental limitations to avoid contradictions. The uncertainty principle helps in this regard. In the quantum world it’s only possible to speak of probability distributions. For example, the position of an electron in space cannot be determined precisely but can only be predicted with a certain probability. The description of the microscopic world is thus not deterministic but statistical in nature. In the progress between classical and quantum physics one sees that in quantum physics one has been able to make the most remarkable of assumptions and that is to discard the notion of causality. And if there´s anything that has been deeper in the hearts of scientists since the Greeks it seems to me it would have been causality. Planck’s discoveries go back more than a century. Yet the laws of quantum mechanics are still surprising and difficult to understand. Nonetheless they govern our daily lives. Lasers, magnetic resonance imaging, computers, none of them would be possible without quantum mechanics or without Schrödinger’s cat in its box.

Abstract

Starting with Erwin Schrödinger’s cat paradox the two-part Mini lecture “Quantum Mechanics” introduces to the central, quantum mechanical principles for the analysis of microscopic elementary particles: Max Planck’s black body radiation theory, Einstein’s photoelectric effect, Bohr's atomic model and the Heisenberg’s matrix mechanics and uncertainty principle. Part two of the Mini Lecture "Quantum Mechanics" discusses Bohr's atomic model and the Heisenberg Uncertainty Principle and highlights the validity of both theorems for present-day quantum physics research.