Abstract-The basic principles of quantum mechanics of the photon, describing its single-particle states by means of the wave function in the coordinate representation are given. This wave function is a wave packet constructed by the superposition of the basic bivectors which are eigenfunctions of the operators of energy, momentum and helicity. The results of modeling in the space-time of such wave packet with a Gaussian distribution on the momentum of the photon corresponding femtosecond laser radiation are discussed. On the basis of the general ideas about the evolution of this packet and within the framework of the constructed photon quantum mechanics the quantum-mechanical approach is proposed to explain the wave phenomena exhibited by light such as the light interference in Young's experiment. It is emphasized that actually the photon isn't some "created" quantum corpuscle, but it's a quasi-particle that is a result of the propagation of spin waves in physical vacuum, the nature of which should be considered at the Planck distances simultaneously with the structure of the leptons and other fundamental particles.
The constantly changing labor market requires the formation of specialists with a desire for self-improvement, capable of moving from one type of activity to another, perhaps not related to the previous one. This task can be called a priority in the field of professional education, which dictates its relevance for mathematics education. When setting the formulated problem and solving it, special attention should be paid to recognizing the importance of the formation and development of the educational potential of the creative activity of students. The article presents an analysis of the possibilities of a continuous education system, put forward theoretical provisions and pedagogical conditions for the effective formation of research skills of students within this system. The characteristic of the structural-content model of the formation of the research competence of future teachers (or specialists of other professions requiring the formation of research competencies) in the system of three-level education is given on the example of studying one of the directions of discrete mathematics.
Abstract-The main principles of photon quantum mechanics describing its one-particle states with the help of the wave function in coordinate representations are given. This wave function (packet) is the superposition of the basic bivectors that are generalized eigenfunctions of energy, momentum, and helicity operators. The quantum-mechanical approach is offered for an explanation of the interference Young's experiment. This explanation is especially important for new interpretation of the non-laser method of obtaining the interference by the amplitude division, as in this case it is traditionally assumed that the radiation of one light train of a single atom interferes with itself. In our explanation, not both "halves" of some real train ("scrap") of the electromagnetic wave interfere with each other, but the both terms of the photon's wave function do this. Nevertheless, the wave function is not directly measured by experience, and therefore it does not exist as a physical object. The attraction of the wave function to the explanation of single-photon interference obtained "by the division of the wave front" is obviously also necessary. Therefore, the situation for the photons emitted by individual atoms (and also, obviously, by laser), is absolutely similar to the situation with the particles having mass, whose distribution in space is described by wave function in coordinate representation. It is pointed out that in fact the photon is not some "formed" quantum particle, but it is a quasi-particle arising when a certain spin wave propagates in a physical vacuum at Planck distances.
В настоящее время интерференционные оптические явления теоретически описываются либо с точки зрения классической электродинамики, либо на языке вторичного квантования. «Первичное квантование» поведения фотона попало под запрет с момента появления работы [1], в которой отрицалась принципиальная возможность построения волновой функции фотона в координатном представлении. Однако в середине 90-х годов предыдущего столетия начали появляться работы [2] -[4], в которых при интерпретации волновой функции фотона был смещен акцент с плотности вероятности локализации фотона на плотность вероятности его обнаружения в некоторой пространственной точке. Очевидно, потребность построения волновой функции фотона в координатном представлении вновь становится актуальной в связи с появлением принципиально новых экспериментов и чисто практических запросов, например, при проверке неравенств Белла и квантовой нелокальности, в квантовой криптографии и вычислениях. Эти эксперименты, в частности, стимулировали разработку источников и детекторов одиночных фотонов. В [6] -[13] и других работах одночастичная волновая функция фотона получила дальнейшее развитие в теоретическом обосновании.В [14] -[20] для ее наглядной иллюстрации проведено моделирование свободного распространения в пространстве волнового пакета, описывающего однофотонное состояние, соответствующее лазерному излучению длительностью 80 фс с центральной длиной волны 10 мкм, с гауссовским распределением по импульсам (фотона), представленным в этом пакете. В результате моделирования установлен характер расплывания волнового пакета: его пространственная форма из первоначальной «шарообразной» формы эволюционирует в некую «конусообразную», напоминая картину излучения Вавилова-Черенкова,
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