Abstract
For a one-dimensional free particle does the set of observables composed of the Hamiltonian and Parity constitute a complete set?
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Notes
- 1.
We see a similar behavior in optics when a change in the refractive index generates a reflected wave. In fact, monochromatic electromagnetic waves, once the time dependence has been removed, are ruled by the same equation, where the term \(2m(V-E)/\hbar ^2\) is replaced by \(k^2/c^2\), where c is the propagation speed, function of the refractive index.
- 2.
The classification in odd and even eigenfunctions can be imposed a priori, since, for a potential invariant for parity, the eigenfunctions of the discrete spectrum have fixed parity.
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Angelini, L. (2019). One-Dimensional Systems. In: Solved Problems in Quantum Mechanics. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-18404-9_2
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DOI: https://doi.org/10.1007/978-3-030-18404-9_2
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