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Elements of Quantum Mechanics

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Book cover A Trajectory Description of Quantum Processes. I. Fundamentals

Part of the book series: Lecture Notes in Physics ((LNP,volume 850))

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Abstract

Bohmian mechanics constitutes a different way to understand quantum mechanics, where the role of an external observer is not present, and quantum phenomena and processes are explained in a causal way, connecting system configurations at different times by means of trajectories. However, in order to better understand the ideas and concepts behind this approach to the quantum world, in this chapter some relevant ingredients from the standard quantum mechanics are briefly revisited. In this regard, special emphasis is made on trajectory-based approaches or their use to obtain quantum-mechanical information directly (calculation of observables) or inferring it from quantum-classical correspondence arguments (phase–space distributions, such as the Wigner and Husimi distributions). Thus, apart from general quantum concepts, the derivation of Schrödinger’s equation by means of the Hamiltonian analogy, the Feynman path integral formulation, the semiclassical route to quantum mechanics or the eikonal approach, will be also briefly exposed.

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Notes

  1. 1.

    Unless otherwise stated, the concept of field function (or, in brief, a field) will be used to denote a function which depends on a set of independent variables.

  2. 2.

    Actually, this point in common between scalar optics and quantum mechanics has allowed that many solutions to problems within the latter were directly adapted from well-known nineteenth century solutions from the former [18].

  3. 3.

    For a more detailed discussion on the properties (and differences) between pure and nonpure or mixed states, see, for example, [28, 29].

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  1. Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006, Madrid, Spain

    Ángel S. Sanz & Salvador Miret-Artés

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Sanz, Á.S., Miret-Artés, S. (2012). Elements of Quantum Mechanics. In: A Trajectory Description of Quantum Processes. I. Fundamentals. Lecture Notes in Physics, vol 850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18092-7_3

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