Sharing symmetries
DOI:
https://doi.org/10.31349/RevMexFis.72.030701Keywords:
Schrödinger equation, symmetries, harmonic oscillator, coherent statesAbstract
Making use of the fact that the solutions of the Schrödinger equation for the harmonic oscillator can be expressed in terms of the solutions of the Schrödinger equation for a free particle, we find the effect on the wavefunctions of the harmonic oscillator produced by the spatial translations and the Galilean transformations on the wavefunctions of a free particle. We find that these symmetry transformations applied to the ground state of the harmonic oscillator produce the coherent states.
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G.F. Torres del Castillo, Relating the free particle with the harmonic oscillator, Rev. Mex. Fís. 71 (2025) (to appear). DOI: https://doi.org/10.31349/RevMexFis.71.030701
G.F. Torres del Castillo and B.C. Nájera Salazar, Transformation of a wavefunction under changes of reference frame, Rev. Mex. Fís. 63 (2017) 185.
K. Gottfried and T.-M. Yan, Quantum Mechanics: Fundamentals, 2nd ed. (Springer, New York, 2003). https://doi.org/10.1007/978-0-387-21623-2. DOI: https://doi.org/10.1007/978-0-387-21623-2
G.F. Torres del Castillo, An Introduction to Hamiltonian Mechanics (Springer, Cham, 2018). https://doi.org/10.1007/978-3-319-95225-3. DOI: https://doi.org/10.1007/978-3-319-95225-3_4
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