Einstein’s 1905 paper on the photoelectric effect, in which he considered Planck’s idea of quanta of energy to be a universal characteristic of light, marks the beginning of quantum theory. Electrons and other quantum particles behave like particles and like waves, depending on the particular observation. An electron occupies a position in space only when an observation is made. Heisenberg decided that the problem of the actual orbits of the electrons inside the atom should be ignored; they have no meaning. Schrodinger reasoned that if an electron has a wave-like behavior, then it should be possible to describe this behavior in space and time by a wave equation. Soon after it was discovered that high-speed electrons had wavelengths that were much shorter than the wavelengths of light, physicists showed that magnetic fields could act as lenses by causing electron waves to converge to a focus.
Einstein’s 1905 paper on the photoelectric effect, in which he considered Planck’s idea of quanta of energy to be a universal characteristic of light, marks the beginning of quantum theory. Electrons and other quantum particles behave like particles and like waves, depending on the particular observation. An electron occupies a position in space only when an observation is made. Heisenberg decided that the problem of the actual orbits of the electrons inside the atom should be ignored; they have no meaning. Schrodinger reasoned that if an electron has a wave-like behavior, then it should be possible to describe this behavior in space and time by a wave equation. Soon after it was discovered that high-speed electrons had wavelengths that were much shorter than the wavelengths of light, physicists showed that magnetic fields could act as lenses by causing electron waves to converge to a focus.
Einstein’s 1905 paper on the photoelectric effect, in which he considered Planck’s idea of quanta of energy to be a universal characteristic of light, marks the beginning of quantum theory. For over ten years Einstein stood alone on the issue of energy quantization of light; and although in 1915 experimental conrmation of his photoelectric effect came from painstaking experiments performed by Millikan, acceptance of the idea that light was composed of particles was far from universal. Millikan himself wrote in 1915: “Despite … the apparent complete success of the Einstein equation, the physical theory of which it was designed to be the symbolic expression is found so untenable that Einstein himself, I believe, no longer holds to it.” Einstein did hold to it. It was only in the mid 1920s, when Heisenberg, Schrödinger, Dirac, and others developed the rst forms of quantum theory, that serious discussions concerning the particle nature of light and the meaning of the new theory began. Discussions about the meaning of quantum theory continue today.
Most textbooks say that quantum mechanics came into being when Max Planck, in a desperate attempt to construct a theory that explained experimental data, explored the radical idea of energy being radiated or absorbed by all bodies in discrete packets (or quanta). The energy content of a quantum of radiation is proportional to the frequency of the radiation emitted or absorbed, as in , and the proportionality constant bears the name of Planck. Planck himself was rather uncomfortable with the idea of energy packets, and spent a considerable amount of time in later years trying to “restore” the classical picture of continuous energy exchange between bodies and surroundings. However, in 1905 Einstein was able to use the idea of the quantum to explain the mechanism of the photoelectric effect, which cannot be explained in any other way! This established the reality of the quantum and so, it may be said that Einstein, rather than Planck, is the father of quantum mechanics. Within a few years, Neils Bohr constructed his model of the hydrogen atom in which the electron can only occupy certain special orbits around the nucleus, and any jump between these orbits is accompanied by energy being absorbed or emitted in the form of quanta. The nearly exact agreement of Bohr’s predictions based on the model and observed hydrogen atomic spectra was among the first impressive accomplishments of quantum mechanics.
At the beginning of the twentieth century, it became clear that microscopic particles do not obey Newton's laws of classical mechanics. The idea of light quanta was at odds with the established wisdom that light is a wave phenomenon, of course, but no other explanation of the photoelectric effect seemed possible. The next step in the development of quantum mechanics was taken by Niels Bohr, who introduced postulates about the discreteness of the energy of the bound electrons in an atom similar to the discreteness of the energy of light quanta. Modern quantum mechanics was founded by Werner Heisenberg, Max Born, Erwin Schroedinger, Paul Adrian Maurice Dirac, Wolfgang Pauli, Enrico Fermi, and others. In quantum mechanics, it is in general fundamentally impossible to determine the exact outcome of an experiment; one can only determine the probability of any given outcome.
The major problem that physicists were trying to solve was that of the wave nature of the electron. In 1926, the Austrian physicist Erwin Schrodinger presented an equation that described the wave behavior of the electron in the hydrogen atom. The physicist Max Born suggested instead that these waves were waves of probability; that is, they represented the probability of finding the electron in some region of space. In fact, an electron has a well-defined position only when it is being observed. Position is not an intrinsic property of an electron. The wave nature of electrons is the basis for the electron microscope, invented in 1932 by Ernst Ruska in Germany. Electron wavelengths are much shorter than those of visible light.
We tried to introduce the idea of quantization in Chapter 9 as a completion of a one semester course. However, we skipped over some really interesting events in the history of Science between 1900 and 1913 when Bohr derived the quantized energy of the H atom. First we want to carry out the 1901 Planck derivation of the formula for blackbody radiation [1]. Many texts just show the curve, write e¼ hn, and move on. As a student, this author found that limited explanation very frustrating since energy quantization is a fundamental concept. Even among graduate texts in quantum mechanics, we are aware of only one that does the complete treatment which we will draw upon for the mathematics [2] but supplement with a narrative that we have found helpful to students over the years. Then in 1905, Albert Einstein (1879-1955), one of the most influential scientists of all time, gave an explanation of the photoelectric effect [3] for which he received the Nobel Prize in 1921. Even reducing our list to essential topics, we need to discuss the Davisson-Germer experiment [4]. The photoelectric effect introduces the idea that light waves can act as particles while the Davisson-Germer experiment showed that particles can act like waves and confirmed the De Broglie equation [5]. However, you can be assured that it will not be as difficult as you might have anticipated and if you can absorb the meaning of just these three key experiments you should be able to begin thinking in terms of quantum mechanics! Despite our slow historical development, this is 2010 and we have to get to the twenty-first century somehow!
At the turn of the 20th century, Max Planck and Albert Einstein introduced the quantum theory which revolutionized our understanding of the nature of energy, in particular the nature of light energy. According to Planck, energy is absorbed or emitted from hot objects in tiny discrete bundles called quanta, and each quantum carries a precise quantity of energy which is related to the frequency of light wave. Einstein generalized Planck’s quantum theory. Einstein’s quantum theory removed a grating asymmetry in nature, between energy and matter. Louis DeBroglie said proposed that if light waves behave as particles, electrons, normally thought of as particles, ought to reciprocally behave as waves. DeBroglie provided a crucial missing piece in the quantum puzzle of discrete Bohr orbitals. Erwin Schroedinger seized DeBroglie’s brain wave. He developed a “wave mechanics” to describe the quantum world. For Schroedinger, particles are just an “illusion” of many waves; he turned waves into particles.