The Historical Development of Quantum Theory

Mehra, Jagdish; Rechenberg, Helmut

doi:10.1007/978-1-4612-5783-7

Cited by 432 publications

(237 citation statements)

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“…The earliest appearance of the non-relativistic continuity equation is due to Schrödin-ger himself [321,2], obtained from his time-dependent wave-equation. A relativistic continuity equation (appropriate to a scalar field and formulated in terms of the field amplitudes) was found by Gordon [322].…”

Section: Background To the Non-relativistic And Relativistic Casesmentioning

confidence: 99%

Complex States of Simple Molecular Systems

Englman¹,

Yahalom²

2002

Advances in Chemical Physics

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A review is given of phase properties in molecular wave functions, composed of a number of (and, at least, two) electronic states that become degenerate at some nearby values of the nuclear configuration. Apart from discussing phases and interference in classical (non-quantal) systems, including light-waves, the review looks at the constructability of complex wave functions from observable quantities ("the phase problem"), at the controversy regarding quantum mechanical phase-operators, at the modes of observability of phase and at the role of phases in some non-demolition measurements. Advances in experimental and (especially) theoretical aspects of Aharonov-Bohm and topological (Berry) phases are described, including those involving two-electron and relativistic systems. Several works in the phase control and revivals of molecular wave-packets are cited as developments and applications of complex-function theory. Further topics that this review touches on are: coherent states, semiclassical approximations and the Maslov index. The interrelation between time and the complex state is noted in the contexts of time delays in scattering, of time-reversal invariance and of the existence of a molecular time-arrow.When the stationary Born-Oppenheimer description for nearly degenerate state is regarded as "embedded" in a broader dynamic formulation, namely through solution of the time dependent Schrödinger equation, the wave function becomes necessarily complex. The analytic behavior of this function in the complex time-plane can be exploited to gain information about the connection between phases and moduli of the componentamplitudes. One form of this connection are a pair of reciprocal (Kramers-Kronig type) relations in the complex time-domain. These show that certain phase changes in a component amplitude (such as, e.g., lead to a non-zero Berry-phase) require changes in the amplitude-moduli, too, and imply degeneracies of the electronic state.The subject of conical degeneracy, or intersection, of adjacent potential surface is extended to nonlinear nuclear-electronic coupling, which can then result in multiple conical degeneracies on a nuclear coordinate plane. We treat cases of double and fourfold intersections, the latter under trigonal symmetry, and employ an analytic-graphical phase tracing method to obtain the resulting Berry phases as the system circles around some or all of the degeneracy points. These phases can take up values that are all integral multiples of π, with integers that vary with the physical situation (or with the model postulated for it).A further type of invariance, with respect to gauge transformation, is also tied to the complex form of the wave function. For a many-component state this leads to a consideration of tensorial (Yang-Mills type) fields F for molecular systems. It is shown that it is the truncation of the Born-Oppenheimer electron-nuclear superposition that generates the molecular Yang-Mills fields.The equations of motion for the nuclear degrees of freedom are derived from a Lagr...

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Section: Background To the Non-relativistic And Relativistic Casesmentioning

confidence: 99%

Complex States of Simple Molecular Systems

Englman¹,

Yahalom²

2002

Advances in Chemical Physics

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“…A polêmica sobre a realidade física dosátomos só encontrou o seu final com os estudos de Einstein e Smoluchowski sobre o movimento browniano [10].…”

Section: A Evolução Da Teoria Atômicaunclassified

“…Outros experimentos foram feitos, porém a explicação do fenômeno só veio com os trabalhos independentes de Einstein de 1905 [12] e de Smoluchowski de 1906 [10].…”

Section: A Evolução Da Teoria Atômicaunclassified

O estudo do movimento browniano com material de baixo custo

Perez

Castro

Maia

et al. 2017

Rev. Bras. Ensino Fís.

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O estudo do movimento browniano é visto em disciplinas de física moderna de cursos de graduação em física, seguindo uma abordagem teórica ou de laboratório, neste caso geralmente envolvendo equipamentos de razoável sofisticação. Neste trabalho é descrita uma proposta de implementação do experimento no ensino médio, pensada e desenvolvida por estudantes do último semestre do curso noturno de licenciatura em Física da Universidade Federal do Pará, como parte das atividades de uma disciplina de Física Estatística. A facilidade da montagem do experimento, aliada ao uso de tecnologias computacionais para a análise dos resultados, faz com que a técnica possa ser facilmente implementada no ensino médio, possibilitando ao estudante discutir aspectos históricos do desenvolvimento dos modelos atômicos, bem como realizar a medição experimental do número de Avogrado, visto usualmente em Química, de forma mecanizada.

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“…As a matter of fact, the textbooks in which physicists learnt quantum mechanics until the 1950s did not "reflect much concern at all about the interpretation of the theory". (10) According to Kragh, "most textbook authors, even if sympathetic to Bohr's ideas, found it difficult to include and justify a section on complementarity. Among fortythree textbooks on quantum mechanics published between 1928 and 1937, forty included a treatment of the uncertainty principle; only eight of them mentioned the complementarity principle".…”

Section: Interpretation Of Quantum Physics -The First Timesmentioning

confidence: 99%

The Historical Roots of ‘‘Foundations of Quantum Physics’’ as a Field of Research (1950–1970)

Freire¹

2004

Found Phys

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The Historical Development of Quantum Theory

Cited by 432 publications

References 0 publications

Complex States of Simple Molecular Systems

Complex States of Simple Molecular Systems

O estudo do movimento browniano com material de baixo custo

The Historical Roots of ‘‘Foundations of Quantum Physics’’ as a Field of Research (1950–1970)

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