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3120 results in Quantum Physics, Quantum Information and Quantum Computation

Page 48 of 156

  • 13 - Identical Particles

  • from Part I - Basics
  • Arjun Berera, University of Edinburgh, Luigi Del Debbio, University of Edinburgh
  • Book:
    Quantum Mechanics
    Published online:
    19 November 2021
    Print publication:
    21 October 2021, pp 182-188

  • Summary

    There are many systems in nature that are made up of several particles of the same species. These particles all have the same mass, charge and spin, and need to be treated as identical particles. For instance, the electrons in an atom are identical particles. Identical particles cannot be distinguished by measuring their intrinsic properties. While this is also true for classical particles, the laws of classical mechanics allow us to follow the trajectory of each individual particle, i.e. their time evolution in space.

  • 16 - Time-Independent Perturbation Theory

  • from Part II - Applications
  • Arjun Berera, University of Edinburgh, Luigi Del Debbio, University of Edinburgh
  • Book:
    Quantum Mechanics
    Published online:
    19 November 2021
    Print publication:
    21 October 2021, pp 268-306

  • Summary

    Very few problems in quantum mechanics can be solved exactly. For example, in the case of the helium atom, including the inter-electron electrostatic repulsion term in the Hamiltonian changes the problem into one which cannot be solved analytically. Perturbation theory provides a method for finding approximate energy eigenvalues and eigenstates for a system whose Hamiltonian is of the form.

  • 3 - Observables

  • from Part I - Basics
  • Arjun Berera, University of Edinburgh, Luigi Del Debbio, University of Edinburgh
  • Book:
    Quantum Mechanics
    Published online:
    19 November 2021
    Print publication:
    21 October 2021, pp 38-66

  • Summary

    In this chapter we are going to set up the formalism to describe observables in quantum mechanics. This is an essential part of the formulation of the theory, as it deals with the description of the outcome of experiments. Beyond any theoretical sophistication, a physical theory is first and foremost a description of natural phenomena; therefore it requires a very precise framework that allows the observer to relate the outcome of experiments to theoretical predictions. As we will see, this is particularly true for quantum phenomena. The necessary formalism is very different from the intuitive one used in classical mechanics. A subtle point is that the state of the system is not an observable by itself. As seen in the , the state of the system is specified by a complex vector.

  • 17 - Calculation Methods Beyond Perturbation Theory

  • from Part II - Applications
  • Arjun Berera, University of Edinburgh, Luigi Del Debbio, University of Edinburgh
  • Book:
    Quantum Mechanics
    Published online:
    19 November 2021
    Print publication:
    21 October 2021, pp 307-339

  • Summary

    There are various calculational methods beyond the perturbation theory of thethat can be applied in specific circumstances to give either exact or approximate results. In this chapter some of the most common methods are explained. We start with the Rayleigh–Ritz variational method that can be used to obtain an upper-bound estimate of the ground-state energy of a quantum-mechanical system. Next we examine multi-electron atoms. In such a case simple application of perturbation theory becomes difficult and more needs to be done.

Page 48 of 156