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CRC Press eBooks

The Early Atomic Theory

Carlos I. Calle

Published Apr 23, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.1201/9780429431029-28

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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.
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.
Quantum mechanics began in very early twentieth century when Max Planck found the expression for black body thermal radiation in which the emitted light was not a continuum as postulated by classical physics. Erwin Schrodinger applied his equation to solve the quantum harmonic oscillator, the quantum rigid rotor, and a hydrogen-like atom. Pertaining to the solution of the Schrodinger equation to hydrogen atoms are the quantum numbers. C. K. Ingold’s overview of Schrodinger wave mechanics: “What can be known about an electron, considered as a particle, is of a statistical nature, and is summarized in the behavior of a wave. When considering singlet substances, the normal Zeeman Effect occurs, providing the discrete values of the orbital angular momentum. In an attempt to rationalize the anomalous Zeeman effect, W. Pauli proposed the fourth degree of freedom of the electron which he called “two-valuedness not describable classically”.
Abstract In June 1925 Heisenberg made the breakthrough that would lead to matrix mechanics. The theory was abstract, offered no means for visualizing the mechanics of the atom, and its application required a lot of heavy lifting. Erwin Schrödinger subsequently made the breakthrough that would lead to wave mechanics, building on Louis de Broglie’s association of a wave with an electron. In Schrödinger’s wave equation the quantum numbers of the hydrogen atom arise naturally. He argued that his ‘wavefunction’ offered a realistic description of the electron in an atom, and sought to eliminate Bohr’s discontinuous quantum jumps. But in the spring of 1926, Max Born offered an enduring alternative. The modulus-square of the wavefunction is a measure of probability in an unvisualizable microphysics. In an intense debate with Bohr, Schrödinger demanded a theory based on logical concepts free from contradictions. Bohr was left to ponder what this might mean.
Till 1925 the idea of what the quantum theory would be was unknown. During 1925 three different but equivalent versions of quantum theory were proposed – Schrödinger-proposed wave mechanics; Heisenberg-developed matrix mechanics and Dirac-introduced operator theory. Considering the de Broglie’s matter waves Erwin Schrödinger, an Austrian physicist, argued that if a particle like an electron behaves as a wave then the equation of wave motion could be successfully applied to it. He postulated a function varying in both space and time in a wave-like manner (hence called wave function and denoted it as ψ). This function is generally complex and assumed to contain information about a system. Schrödinger set up a linear and time-dependent wave-like equation, called Schrödinger wave equation, to describe the wave aspect of a particle taking account of de Broglie’s relation for wavelength. Physically, |ψ(X, t)|2, where ψ(X, t) is the solution of the Schrödinger equation, is interpreted as position probability density. That is, |ψ(X, t)|2 is the probability density of observing a particle at position X at time t. ψ does not give exact outcomes of observations but helps us to know all possible events and their probabilities . Further, the probability interpretation allows us to find the average or expected result of a set of measurements on a quantum system.
Abstract While the theory proved successful at describing a broad range experimental results, from the black body spectrum to the hydrogen atom, the question arose as to what the theory was telling us about the nature of physical reality. Schrödinger’s attempt to represent particles as wave packets failed because of the spreading of the wave packets. Max Born, investigating how the theory could be applied to scattering processes, was led to introduce the probability interpretation of the wave function. In an attempt to summarize the physical meaning of the theory, Heisenberg introduced the uncertainty principle. Niels Bohr and his Copenhagen school developed the philosophical position known as “complementarity.” There was a bitter dispute between Schrödinger and the “Copenhageners” over the necessity of quantum jumps in the theory.
During 1925 three different but equivalent versions of quantum theory were proposed, Schrodinger proposed wave mechanics; Heisenberg developed matrix mechanics and Dirac-introduced operator theory. Considering the de Broglie's matter waves Erwin Schrödinger, an Austrian physicist, argued that if a particle like an electron behaves as a wave then the equation of wave motion could be successfully applied to it. He postulated a function varying in both space and time in a wave-like manner. Schrodinger set up a linear and time-dependent wave-like equation, called Schrodinger wave equation, to describe the wave aspect of a particle taking account of de Broglie's relation for wavelength. This chapter discusses the Schrodinger equation and explores the general properties of the solution of the Schrodinger equation. It verifies the Ehrenfest's theorem in certain interesting systems and solves equation for linear harmonic oscillator and shows that their solutions are identical to the solutions of classical equation of motion.