Thesis (M.A.)--University of Wisconsin--Madison, 1966. / Title from title screen (viewed June 29, 2009). Includes bibliographical references. Online version of print original.

Thesis (M.A.)--University of Wisconsin--Madison, 1966. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued that the de Broglie-Bohm theory is of notable interest to physics. Using the causal theory, electron trajectories are found for the conventional Schr??dinger, Pauli and Dirac hydrogen eigenstates. In the Schr??dinger case, an additional term is used to account for the spin; this term was not present in the original formulation of the theory but is necessary for the theory to be embedded in a relativistic formulation. In the Schr??dinger, Pauli and Dirac cases, the eigenstate trajectories are shown to be circular, with electron motion revolving around the <i>z</i>-axis. Electron trajectories are also found for the 1<i>s</i>-2<i>p</i>0 transition problem under the Schr??dinger equation; it is shown that the transition can be characterized by a comparison of the trajectory to the relevant eigenstate trajectories. The structures of the computed trajectories are relevant to the question of the possible evolution of a quantum distribution towards the standard quantum distribution (quantum equilibrium); this process is known as quantum relaxation. The transition problem is generalized to include all possible transitions in hydrogen stimulated by semi-classical radiation, and all of the trajectories found are examined in light of their implications for the evolution of the distribution to the standard distribution. Several promising avenues for future research are discussed.

Orientador: Roberto de Andrade Martins / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-09-25T12:34:08Z (GMT). No. of bitstreams: 1 Rosa_PedroSergio_M.pdf: 2456549 bytes, checksum: 778fc09658778fcab5b7c88086506af9 (MD5) Previous issue date: 2004 / Resumo:Este trabalho estuda a história do conceito da dualidade onda-partícula, do início do século XX (trabalhos de Albert Einstein) até o surgimento da teoria de Louis de Broglie. O primeiro capítulo descreve a história inicial da teoria quântica, do estudo da radiação do corpo negro até 1909, dando ênfase especialmente às idéias de Einstein a respeito da natureza da luz, e outras interpretações corpusculares da radiação (William Bragg, J. J. Thomson e Johannes Stark). Nenhuma dessas propostas pode ser descrita como uma síntese dos conceitos de onda e partícula. O segundo capítulo descreve os principais episódios relevantes de 1909 até 1922. Durante esse período, a teoria quântica teve um forte desenvolvimento, especialmente após a Conferência Solvay de 1911 e depois do surgimento da teoria de Niels Bohr sobre os espectros atômicos. No entanto, a natureza do quantum e da radiação permaneceram obscuras. Entretanto, pesquisas sobre raios X trouxeram o problema da dualidade à tona, porque essa radiação exibe de um modo notável várias propriedades corpusculares, embora também exiba propriedades ondulatórias na difração por cristais. A descoberta do efeito Compton em 1922-1923 foi também uma fortíssima evidência a favor da natureza corpuscular dos raios x. Os capítulos seguintes descrevem o trabalho de Louis de Broglie. Seu ponto de partida foi o estudo experimental dos raios X, no laboratório de seu irmão (Maurice). Em 1922, De Broglie publicou seus primeiros estudos teóricos sobre os quanta de luz, e no ano seguinte desenvolveu as idéias fundamentais de sua teoria sobre a dualidade onda-partícula tanto para a luz quanto para a matéria. Os primeiros trabalhos de Louis de Broglie são analisados no capítulo 3, e sua tese de doutoramento, apresentada em 1924, é discutida no capítulo 4. A principal contribuição da presente dissertação é a análise detalhada dos trabalhos de De Broglie, de 1922 a 1924. O último capítulo apresenta uma breve visão de desenvolvimentos posteriores, tais como a conflrlnação experimental das propriedades ondulatórias dos elétrons e a influência da teoria de De Broglie sobre Schrõdinger / Abstract:This work studies the history of the concept of wave-particle duality , from the beginning of the 20th century (Albert Einstein's works) to the emergence of Louis de Broglie's theory. The flfSt chapter describes the early history of quantum theory, from the study of black-body radiation to 1909, with special emphasis upon Einstein's ideas about the nature of light and other corpuscular interpretations of radiation (William Bragg, J. J. Thomson and Johannes Stark). None of those proposals can be described as a synthesis of the wave and particle concepts. The second chapter describes the main relevant episodes from 1909 to 1922. During this period, quantum theory underwent a strong development, especially after the Solvay Conference of 1911 and Niels Bohr' s theory of atomic spectra. The nature of the quantum and of radiation, however, remained obscure. Research on X rays, however, brought the duality problem to the front position, because this radiation exhibited in a remarkable way several corpuscular properties, while it also displayed wave properties in crystal diffraction. The discovery of the Compton effect in 1922-1923 was also a very strong evidence for the corpuscular nature of X rays. The following chapters describe the work of Louis de Broglie. His starting point was the experimental study of X rays, in his brother' s (Maurice) laboratory .In 1922, de Broglie published his first theoretical studies about light quanta, and in the next year he developed the fundamental ideas of his theory of wave-particle duality for both light and matter. Louis de Broglie's flfSt papers are analyzed in chapter 3, and his PhD thesis, presented in 1924, is discussed in chapter 4. The detailed analysis of de Broglie' s works from 1922 to 1924 is the main contribution of the present dissertation. The last chapter gives a brief survey of later developments, such as the experimental confirmation of the wave properties of electrons and the influence of de Broglie' s theory upon Schrõdinger / Mestrado / Física / Mestre em Física

The de Broglie-Bohm causal interpretation of quantum mechanics is discussed, and applied to the hydrogen atom in several contexts. Prominent critiques of the causal program are noted and responses are given; it is argued that the de Broglie-Bohm theory is of notable interest to physics. Using the causal theory, electron trajectories are found for the conventional Schrödinger, Pauli and Dirac hydrogen eigenstates. In the Schrödinger case, an additional term is used to account for the spin; this term was not present in the original formulation of the theory but is necessary for the theory to be embedded in a relativistic formulation. In the Schrödinger, Pauli and Dirac cases, the eigenstate trajectories are shown to be circular, with electron motion revolving around the <i>z</i>-axis. Electron trajectories are also found for the 1<i>s</i>-2<i>p</i>0 transition problem under the Schrödinger equation; it is shown that the transition can be characterized by a comparison of the trajectory to the relevant eigenstate trajectories. The structures of the computed trajectories are relevant to the question of the possible evolution of a quantum distribution towards the standard quantum distribution (quantum equilibrium); this process is known as quantum relaxation. The transition problem is generalized to include all possible transitions in hydrogen stimulated by semi-classical radiation, and all of the trajectories found are examined in light of their implications for the evolution of the distribution to the standard distribution. Several promising avenues for future research are discussed.

The aim of this thesis was to simulate a part of a proposed experiment by Lev Vaidman by using Bohmian mechanics. To do this a numerical method for solving the Schrödinger equation and theguiding equation was created, with several ways of making the simulation more efficient.To make the simulation work more efficiently the Schrödinger equation was applied to only a small region of the whole setup. This region followed the wavefunction of significant values and could change size during the simulation. A beam splitter was constructed in the form of a thin potential barrier. The beam splitter was tested to verify that the reflected and transmitted angles agreed with expectations. A virtual detector was constructed and used for the calibration of the beam splitter to determine which potential resulted in dividing the wave packet into two wave packets of equal intensity. A fixed angle mirror was used for testing the reflection of a wave packet for the reflected angle and concluded that it agreed with the expectations for it. Testing a time dependent mirror for different frequencies and amplitudes was performed, with the result that the numerical method could be used to determine the particles’ trajectories. These results were used to construct a larger setup that was a small part of Vaidman’s proposed experiment. These setups were done in several version. All setups had one wave packet that went through one beam splitter and separated into two wave packets. These two wave packets reflected at two mirrors with different frequencies and then interfered with each other at either free space or at another beam splitter. The result of the simulation of these setups was that the particles’ trajectories could be calculated with the guiding equation. / Syftet med denna avhandling var att simulera en del av det föreslagna experimentet av Lev Vaidman med hjälp av Bohmsk mekanik. För att göra detta skapades en numerisk metod för att lösa Schrödingerekvationen och den ledande ekvationen, ”the guiding equation”, med flera sätt att effektivisera simuleringen. För att effektivisera simuleringen tillämpades Schrödingerekvationen på endast en liten region i hela uppställningen. Denna region följde vågfunktionen med betydande värden och kunde ändra storlek under simuleringen.En stråldelare konstruerades i form av en tunn potentialbarriär. Stråldelaren testades för att verifiera attde reflekterade och överförda vinklarna överensstämde med förväntningarna. En virtuell detektorkonstruerades och användes för kalibrering av stråldelaren för att bestämma vilken potential som resulterade i att vågpaketet delades in i två vågpaket med samma intensitet.En spegel med fast vinkel användes för att testa reflektionen av ett vågpaket för den reflekterade vinkeln och kom fram till att den överensstämde med förväntningarna för den. Att testa en tidsberoendespegel för olika frekvenser och amplituder utfördes med resultatet att den numeriska metoden kunde användas för att bestämma partiklarnas banor. Dessa resultat användes för att konstruera en större uppställning av ett experiment som var en liten delav Vaidmans föreslagna experiment. Dessa uppställningar gjordes i flera versioner. Alla uppställningar hade ett vågpaket som gick igenom en stråldelare och separerades i två vågpaket. Dessa två vågpaket reflekterades vid två speglar med olika frekvenser och interfererade sedan varandra antingen i en tom rymd eller vid en annan stråldelare. Resultatet av simuleringen av dessa inställningar var att partiklarnas banor kunde beräknas med ledande ekvation.

Ce mémoire examine de façon critique les réflexions apportées par Louis de Broglie (1892-1987) à la compréhension du passage de la mécanique classique à la mécanique quantique. Après avoir cerné la dichotomie onde-corpuscule instaurée en mécanique classique par la théorie corpusculaire newtonienne et ondulatoire maxwellienne, nous examinons comment, selon de Broglie, la coexistence ou la corrélation des ondes et des corpuscules dans la matière a permis de dépasser cette contradiction et de fonder la mécanique ondulatoire et quantique sur de nouvelles bases. Suite à la présentation de la synthèse broglienne de la mécanique ondulatoire, il ressort de cette analyse que le passage de la mécanique classique à la mécanique quantique résulte de l’évolution du concept de matière. L’onde et le corpuscule de la mécanique classique cèdent désormais la place à la « particule-quanton ». À partir de ce monisme quantique, nous avons analysé, dans la dernière partie de ce travail, les implications épistémologiques de la philosophie scientifique de de Broglie. L’intervention du quantum d’action ayant remis en cause les fondements de la mécanique classique, la modification de ces principes a pour corollaire la crise de l’objectivité mécanique et l’échec du mécanisme classique. / This Master’s thesis critically examines the reflections brought by Louis de Broglie (1892-1987) to the understanding of the transition from classical to quantum mechanics. Afterhaving identified the wave-corpuscule dichotomy established in classical mechanics by Newtonian and Maxwellian corpuscular and wave theory, we examine how, according to de Broglie, the coexistence or correlation of waves and corpuscles in matter made it possible to overcome this contradiction and to base wave and quantum mechanics on new foundations. Following the presentation of the broglian synthesis of wave mechanics, it emerges from this analysis that the transition from classical to quantum mechanics results from the evolution ofthe concept of matter. The wave and corpuscle of classical mechanics are now giving way to the “quantum particle”. From this quantum monism, we have analyzed, in the last part of this work, the epistemological implications of de Broglie's scientific philosophy. The intervention of the quantum of action having called into question the foundations of classical mechanics, the modification of these principles has as a corollary the crisis of mechanical objectivity and the failure of the classical mechanism.

Unique français parmi les fondateurs de la mécanique quantique, Louis de Broglie est une figuremajeure de l’histoire de la physique française du XXème siècle. Il devient grâce à son prix Nobel dephysique en 1929 le personnage central de la physique théorique française. Dans les récits usuelsportant sur la physique française du XXème siècle, la mécanique quantique est décrite comme s’étanttrès lentement diffusée en France, et il est souvent admis que peu de physiciens de ce pays l’utilisèrentavant la fin de la seconde guerre. De Broglie est souvent désigné comme le grand responsable de cetétat de fait et est dépeint comme un représentant type d’une pratique de physique théorique obsolète.De plus, son rôle institutionnel et sa responsabilité dans l’isolationnisme français sont dénoncés.Le but de ce travail est, premièrement, d’éclairer les modalités de la diffusion de la mécaniquequantique en France et le rôle de Louis de Broglie dans ce processus. Ce faisant, mon propos apporterade fortes nuances aux habituels récits portant sur cet aspect de l’histoire de la physique française duXXème siècle. Deuxièmement, je montrerai que l’essor de domaines tels que la physique des particules,la physique du solide et la physique nucléaire après la seconde guerre mondiale introduit unchangement dans les pratiques des jeunes théoriciens par rapport aux pratiques qui régnaient autour deLouis de Broglie. Je serai alors en mesure d’expliquer pourquoi l’héritage de Louis de Broglie au seinde la physique française de la seconde moitié du XXème siècle est si peu revendiqué, tout en évitant detomber dans le piège des jugements rétrospectifs et péjoratifs. / As the only Frenchman among the founding fathers of quantum mechanics, Louis de Broglie has agreat importance in the XXth French physics. With the prestige from the Nobel Prize in 1929, deBroglie became the main characters of the French theoretical physics community since the 30’s andgreat responsibilities on its evolution were entrusted to him. In the usually story of the XXth Frenchphysics, quantum mechanics, which is the core of theoretical physics since 1925, is said to have spreadslowly in France and French theorists who really used it were few before WWII. This story goes on,saying that de Broglie was the principal guilty of this state of fact. In this story, the discoverer ofwave-particle duality of matters becomes a representative of old-fashioned theorists who practice anaive kind of picture-based physics. Furthermore, his institutional action and his responsibility in theisolation of French physics are stigmatized.The aim of this work is, firstly, to throw light on the modality of the diffusion of quantummechanics in France and the role of de Broglie in this process, both on the intellectual and theinstitutional side. Secondly, it will be shown that progress in the area of particle physics, solid statephysics and nuclear physics after WWII introduce a shift in the practice of many young theoristsrelative to the way of practice theoretical physical inside de Broglie’s group. We will thus be able tounderstand why the legacy of Louis de Broglie is not claimed in contemporary French theoreticalphysics without falling into the trap of a retrospective and pejorative assessment of the career of themost famous French theorist of the XXth century.

[EN] This thesis aims to find out the applicability of Lorentzian geometry to represent the motion of the electron in hydrogen atoms according to the de Broglie-Bohm quantum theory (dBB). It starts from the observation that electrons behave differently when they are part of atomic systems than when they are unbound. While these, when describing curvilinear trajectories emit energy, in electrons bounded to hydrogen atoms according to dBB describe circular stationary trajectories, without energy emission. The above consideration suggests the hypothesis that electrons bounded to hydrogen atoms move in curved spaces, in which their trajectories are geodesics and therefore without acceleration or energy emission that would imply instability of matter. We use Lorentzian geometry and some heuristic concepts of Einstein's Theory of General Relativity to describe this space-time. Furthermore, we establish an equivalence in the differential field by the tetravelocity and use Levi-Civita connectors, which unify metric and affine geodesics. We thus arrive at the formulation of a theorem and several corollaries that affect the components of the metrics that satisfy the previous hypothesis. These metrics must also achieve the condition of being common to all possible trajectories of electrons of the same magnetic quantum state and two additional hypotheses: that the scalar curvature is positive (in order to avoid geodesic trajectories that escape to infinity) and that the energy component of the momentum-energy tensor corresponding to the Einstein field equations is positive, since although, in principle, this is inapplicable to quantum systems, modern modifications suggest that it is a plausible assumption. With these conditions, we undertake the search for metrics that meet the aforementioned restrictions. We start with two simple metrics that meet the requirements of common space-time and the geodesic character of the trajectories, but the curvature and the energy component of the momentum-energy tensor are negative, so we go to use an exact solution of Einstein's field equations corresponding to a space-time created by particles turning around an axis (Lanczos-Van Stockum metric). We then obtain two metrics that correct the defects of the previous ones, but their geodesics do not exactly get the condition of circularity. Finally, we perform a synthesis of both models and obtain two metrics that reasonably accomplish the requirements, with which we achieve the proposed goal of representing the motion of hydrogen electrons according to the dBB theory in a Lorentzian geometry. The quantum potential of the dBB theory then appears as that which, together with the electromagnetic potential of the nucleus, forms a resulting force that makes rotate the electron around an axis passing through the nucleus. In the Lorentzian formulation proposed in this work, this function is exerted by the curvature of space-time. We also derive from our heuristic hypotheses that the wave-corpuscle duality in dBB theory, with our considerations, exerts a bidirectional interaction beyond the mere passive role that the particle plays in this theory: wave and particle remain at the same level interacting one on the other and vice versa, dialectally. This work is complemented by a historical introduction, focusing particularly on the de Broglie's thesis and the Schrödinger's deduction of his famous equation of eigenvalues, emphasizing the use of a Riemannian metric. In addition, there are epistemological reflections on physical theories focusing on dialectics, and the free creation of concepts, as could be the case in some parts of our work. / [CAT] Aquesta tesi s'adreça a esbrinar l'aplicabilitat de la geometria lorentziana per a representar el moviment de l'electró en àtoms hidrogenoides segons la teoria quàntica de de Broglie-Bohm (dBB). Parteix de la constatació que els electrons es comporten de manera diferent quan formen part de sistemes atòmics que quan són no lligats. Mentre que aquests, quan descriuen trajectòries curvilínies emeten energia, en els electrons lligats a àtoms hidrogenoides segons dBB descriuen trajectòries circulars de manera estacionària, sense emissió energètica. L'anterior consideració ens suggereix la hipòtesi que els electrons lligats a àtoms hidrogenoides es mouen en espais corbats, en què llurs trajectòries en són geodèsiques i per tant sense acceleració ni emissió energètica que implicarien inestabilitat de la matèria. Utilitzem la geometria lorentziana i alguns conceptes de la Teoria de la Relativitat General d'Einstein, amb caràcter heurístic, per a descriure aquest espai-temps. Establim una equivalència en l'àmbit diferencial mitjançant la tetravelocitat i utilitzem connectors de Levi-Civita, que unifiquen les geodèsiques mètriques i les afins. Arribem així a la formulació d'un teorema i diversos corol·laris que afecten els components de les mètriques que satisfan l'anterior hipòtesi. Aquestes mètriques han de complir a més la condició de ser comuns a totes les possibles trajectòries dels electrons del mateix estat quàntic magnètic i de dues hipòtesis addicionals: que la curvatura escalar siga positiva (per tal d'evitar trajectòries geodèsiques que escapen a l'infinit) i que siga positiu el component energètic del tensor d'impulsió-energia corresponent a l'equació de camp d'Einstein, puix encara que aquesta és inaplicable als sistemes quàntics, modernes modificacions fan pensar que és una suposició plausible. Amb aquests condicionants emprenem la recerca de mètriques que complisquen les restriccions adés esmentades. Comencem amb dues mètriques senzilles que compleixen el requisit de l'espai-temps comú i del caràcter geodèsic de les trajectòries, però la curvatura i el component energètic del tensor d'impulsió-energia hi són negatius, per la qual cosa acudim a utilitzar una solució exacta de les equacions de camp d'Einstein corresponents a un espai-temps creat per partícules que giren al voltant d'un eix (mètrica de Lanczos-Van Stockum). Aleshores obtenim dues mètriques que corregeixen els defectes de les anteriors, però llurs geodèsiques no compleixen exactament la condició de circularitat. Finalment realitzem una síntesi d'ambdós models i obtenim dues mètriques que compleixen raonablement els requisits, amb les quals atenyem l'objectiu proposat de representar el moviment dels electrons hidrogenoides segons la teoria dBB en una geometria lorentziana. El potencial quàntic de la teoria dBB, apareix llavors com a aquell que, junt a l'electromagnètic del nucli, configura una força resultant que fa girar l'electró al voltant d'un eix que passa pel nucli. En la formulació lorentziana proposada en aquest treball, aquesta funció és exercida per la curvatura de l'espai-temps. També derivem de les nostres hipòtesis heurístiques que la dualitat ona-corpuscle en la teoria dBB amb les nostres consideracions exerceix una interacció bidireccional més enllà del mer paper passiu que té la partícula en aquesta teoria: ona i partícula resten al mateix nivell interactuant una sobre l'altra i vici-versa de manera dialèctica. / [ES] Esta tesis se dirige a investigar la aplicabilidad de la geometría lorentziana para representar el movimiento del electrón en átomos hidrogenoides según la teoría cuántica de de Broglie-Bohm (dBB). Parte de la constatación de que los electrones se comportan de manera diferente cuando forman parte de sistemas atómicos o cuando son no ligados. Mientras que estos, cuando describen trayectorias curvilíneas emiten energía, en los electrones ligados en átomos hidrogenoides según dBB describen trayectorias circulares de manera estacionaria, sin emisión energética. La anterior consideración nos sugiere la hipótesis de que los electrones ligados a átomos hidrogenoides se mueven en espacios curvos, donde sus trayectorias son geodésicas y por lo tanto sin aceleración ni emisión energética que implicarían inestabilidad de la materia. Utilizamos la geometría lorentziana y algunos conceptos de la Teoría de la Relatividad General de Einstein con carácter heurístico, para describir este espacio-tiempo. Establecemos una equivalencia a nivel diferencial mediante la tetravelocidad y utilizamos conectores de Levi-Civita, que unifican las geodésicas métricas y las afines. Llegamos así a la formulación de un teorema y algunos corolarios que afectan a los componentes de las métricas que satisfacen la anterior hipótesis. Estas métricas han de cumplir además la condición de ser comunes a todas las posibles trayectorias de los electrones del mismo estado cuántico magnético y de dos hipótesis adicionales: que la curvatura escalar sea positiva (para evitar trayectorias geodésicas que escapen al infinito y que sea positivo el componente energético del tensor de impulsión- energía correspondiente a la ecuación de campo de Einstein, porque aunque esta es inaplicable a los sistemas cuánticos, modernas modificaciones sugieren que es una suposición plausible. Con estos condicionantes emprendemos la búsqueda de métricas que cumplan las restricciones mencionadas. Empezamos con dos métricas sencillas que cumplen el requisito del espacio-tiempo común y el carácter geodésico de las trayectorias, pero la curvatura y el componente energético del tensor de impulsión-energía son negativos, por lo que acudimos a utilizar una solución exacta de las ecuaciones de campo de Einstein correspondientes a un espacio-tiempo creado por partículas que giran alrededor de un eje (métrica de Lanczos-Van Stockum). Obtenemos así dos métricas que corrigen los defectos de las anteriores, pero sus geodésicas no cumplen exactamente la condición de circularidad. Finalmente realizamos una síntesis de ambos modelos y obtenemos dos métricas que cumplen razonablemente los requisitos, con las que alcanzamos el objetivo propuesto de representar el movimiento de los electrones hidrogenoides según la teoría dBB en una geometría lorentziana. El potencial cuántico de la teoría dBB aparece entonces como el que, junto al electromagnético del núcleo, configura una fuerza resultante que hace girar al electrón alrededor de un eje que pasa por el núcleo. En la formulación lorentziana propuesta en este trabajo, esta función es ejercida por la curvatura del espacio-tiempo. También derivamos de nuestras hipótesis heurísticas que la dualidad onda-partícula en la teoría dBB con nuestras consideraciones ejerce una interacción bidireccional más allá del mero papel pasivo que tiene la partícula en esta teoría: onda y partícula quedan al mismo nivel interaccionando una sobre la otra y viceversa de manera dialéctica. El trabajo se complementa con una introducción histórica, incidiendo particularmente en la tesis de de Broglie y en la deducción de Schrödinger de su famosa ecuación de valores propios, destacando el uso de una métrica riemanniana. Además, se hacen unas reflexiones epistemológicas sobre las teorías físicas incidiendo en la dialéctica y la libre creación de conceptos, como podría ser el caso. / Gómez Blanch, G. (2021). Varietats lorentzianes en la representació dels estats estacionaris dels àtoms hidrogenoides en la teoria de de Broglie - Bohm. Uns models heurístics [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/176757 / TESIS

Il est peu connu que les problèmes de dynamique quantique peuvent être résolus au moyen de trajectoires, issues de l'interprétation Bohmienne de la mécanique quantique. La propagation numérique de ces trajectoires quantiques constitue cependant un véritable défi, du fait de la difficulté d'évaluer précisément les dérivées spatiales mises<br />en jeu dans les équations. Dans cette thèse nous présentons des approximations permettant de propager les trajectoires quantiques sans instabilités numériques. Nous nous intéressons particulièrement aux systèmes constitués de plusieurs états électroniques couplés. D'une part, nous développons une approximation semi-classique qui découple partiellement la propagation des trajectoires des transitions<br />inter-états. D'autre part, nous appliquons aux systèmes à plusieurs états une reformulation des équations hydrodynamiques en termes de dérivées spatiales. Dans les deux cas, le formalisme est établi puis appliqué numériquement à des processus modèles.