Quantum Mechanics Brings Uncertainty to the Atom: de Broglie, Schrödinger, Heisenberg, Dirac and Born (France, Switzerland, England, Austria, and Germany)
In 1924, Prince Louis-Victor de Broglie proposed the “wave-particle duality of matter”, after which Erwin Schrödinger treated electrons in atoms as confined waves that set up certain allowed wave patterns with corresponding energies described by “quantum numbers”. His wave equation, one of the most important in atomic history, is prominently inscribed above his grave in the picturesque Austrian town of Alpbach and below his bust at the Arcades of the University of Vienna. The story of the “erotic outburst” that produced it is truly unique and one that travelers will revel in recalling when they visit Schrödinger sites. The role of probability and uncertainty in the interpretation of Schrödinger's “wave mechanics”, Heisenberg's “matrix mechanics” and Dirac's relativistic quantum mechanics is discussed in sufficient detail that travelers can begin to appreciate how they are incorporated into modern atomic theory. The nature of atomic orbitals as depictions of the probability of finding electrons in atoms is succinctly explained. Stories about Schrödinger's cat, Dirac's personality, Heisenberg's retreat to the North Seas island Helgoland where he invented “matrix mechanics”, and the enigmatic equation on Max Born's tombstone all contribute to the fun and adventure of traveling with the atom.
In 1924, Prince Louis-Victor de Broglie proposed the “wave-particle duality of matter”, after which Erwin Schrödinger treated electrons in atoms as confined waves that set up certain allowed wave patterns with corresponding energies described by “quantum numbers”. His wave equation, one of the most important in atomic history, is prominently inscribed above his grave in the picturesque Austrian town of Alpbach and below his bust at the Arcades of the University of Vienna. The story of the “erotic outburst” that produced it is truly unique and one that travelers will revel in recalling when they visit Schrödinger sites. The role of probability and uncertainty in the interpretation of Schrödinger's “wave mechanics”, Heisenberg's “matrix mechanics” and Dirac's relativistic quantum mechanics is discussed in sufficient detail that travelers can begin to appreciate how they are incorporated into modern atomic theory. The nature of atomic orbitals as depictions of the probability of finding electrons in atoms is succinctly explained. Stories about Schrödinger's cat, Dirac's personality, Heisenberg's retreat to the North Seas island Helgoland where he invented “matrix mechanics”, and the enigmatic equation on Max Born's tombstone all contribute to the fun and adventure of traveling with the atom.
Abstract In addition to recounting some contemporary scientific history, Chapter 6 describes the hypothesis that matter, like light, can display wavelike properties, and the creation of the various formulations of quantum mechanics. That matter could have a wavelength was proposed in 1924 by Louis de Broglie, who presented a specific formula for calculating it, one that was verified experimentally in 1927. However, de Broglie’s hypothesis was overshadowed by the creation of three versions of quantum mechanics in 1925/26. The first, denoted matrix mechanics, was proposed by Werner Heisenberg. It was quickly and successfully applied by Wolfgang Pauli to the hydrogen atom. Paul Dirac introduced the next version, which was followed by that of Erwin Schrödinger via a wave equation whose solutions, denoted wave functions, were soon interpreted byMax Born to be related to the probability that certain outcomes or events will occur: classical-physics determinism was thereby removed from quantum mechanics.
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 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.
The important discoveries and events that occurred in the development of quantum mechanics may be ordered as follows: Blackbody radiation formulated by Max Planck in 1901. Photoelectric effect interpreted by Albert Einstein in 1905. Model of the atom proposed by Ernest Rutherford in 1911. Quantum theory of atomic spectra developed by Niels Bohr in 1913. Photon–electron scattering experiments done by Arthor Holly Compton in 1922. Exclusion principle proposed by Wolfgang Pauli in 1925. Matter waves proposed by Prince Louis Victor de Broglie in 1925. Wave equation proposed by Erwin Shrödinger in 1926. Electron diffraction experiments done by Clinton Joseph Davisson and L.H. Germer in 1927. Uncertainty principle proposed by Werner Karl Heisenberg in 1927. Interpretation of the wave function done by Max Born in 1927. Relativistic wave equation proposed by Paul A. M. Dirac in 1928.
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.
High Resolution Image Download MS PowerPoint Slide In July 1925, Werner Heisenberg submitted a paper to Zeitschrift für Physik entitled ‘On quantum-theoretical reinterpretation of kinematic and mechanical relationships’, thus giving birth to quantum mechanics. In the following year, building on de Broglie’s wave-particle duality, Erwin Schrödinger developed wave mechanics, and soon, Max Born provided a probabilistic interpretation of the wave function. The theory was further enriched by the exclusion principle of Wolfgang Pauli and the uncertainty principle of Heisenberg, which ultimately led to the development of relativistic quantum mechanics by Dirac. The Copenhagen Interpretation created a probabilistic framework for understanding the theory. Over the past century, quantum mechanics has paved the way for advances in quantum field theory, computing, and modern technologies. This historical narrative provides insights into the complex discovery process that led to the development of quantum mechanics, which can potentially guide novel breakthroughs amid challenging conceptual struggles, as seen in the field of artificial intelligence today.