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Motion of Particles

Chapter
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Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Abstract

In this chapter, we will explore how to describe the position and momentum of a particle in quantum mechanics, and how we set up its Schrödinger equation. To this end, we need to work out how to describe the momentum and energy for a particle. We will conclude with a description of a bizarre phenomenon called quantum tunnelling, which is now widely used in advanced microscopes, and with a qualitative overview of the quantum mechanical foundations of chemistry.

Supplementary material

460544_1_En_8_MOESM1_ESM.zip (326 kb)
Supplementary material 1: Towards a continuum of probability densities (zip 326 KB)
460544_1_En_8_MOESM2_ESM.zip (194 kb)
Supplementary material 2: The Dirac delta function (zip 193 KB)
460544_1_En_8_MOESM3_ESM.zip (4.6 mb)
Supplementary material 3: Building up the diffraction pattern with individual electrons. Courtesy of the Central Research Laboratory, Hitachi, Ltd. Japan (zip 4720 KB)
460544_1_En_8_MOESM4_ESM.zip (363 kb)
Supplementary material 4: The effect of the barrier on quantum tunnelling (zip 362 KB)
460544_1_En_8_MOESM5_ESM.zip (519 kb)
Supplementary material 5: Probability densities for the electron in hydrogen (zip 518 KB)
460544_1_En_8_MOESM6_ESM.zip (5.3 mb)
Supplementary material 6: The periodic table of elements (zip 5433 KB)

References

  1. G. Binnig, H. Rohrer, Scanning tunneling microscopy. IBM J. Res. Dev. 30, 355 (1986)Google Scholar
  2. L. de Broglie, Recherches sur la théorie des quanta, Ph.D. thesis, Paris 1924; Ann. de Phys. 3(22) (1925)Google Scholar
  3. W. Heisenberg, Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Z. Phys. 33, 879 (1925)ADSCrossRefGoogle Scholar
  4. W. Pauli, Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren, Z. Phys. 31, 765 (1925)ADSCrossRefGoogle Scholar
  5. E. Schrödinger, An undulatory theory of the mechanics of atoms and molecules. Phys. Rev. 28, 1049 (1926)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of SheffieldSheffieldUK

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