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Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2018, Tutor: Oleg Bulashenko

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We discuss the possibility to build the formalism of quantum mechanics based on Parity-Time (PT ) symmetry, rather than on the Hermiticity of operators. We consider the simple analytically tractable case of a PT -symmetric 2 x 2 Hamiltonian matrix and analyse the conditions for the eigenvalues to be real and for time evolution to be unitary. Lastly, we review and reproduce the results of an experiment involving PT symmetry in optics