An Introduction To Non-Hermitian Quantum Mechanics


Thursday, 16th September 2021 at 4.00 pm through MICROSOFT TEAMS

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Quantum mechanics is formulated in terms of self-adjoint or Hermitian operators which guarantees that the Ham-iltonian of a system must exhibit real eigenvalues and lead to conservation of probability [1]. However, in case of open systems, there may be an exchange of energy/particles among the subsystems and one can encounter an overall growth or decay in energy or probability norm. Such energy non-conserving or dissipative systems can be modelled through the adoption of non-Hermitian Hamiltonians and described within the framework of non-Hermitian quantum mechanics (NHQM). NHQM has become an important alternative to the standard (Hermitian) formalism of quantum mechanics and has applications in a variety of fields [2]. In recent years, Bender and co-workers have demonstrated that parity-time (PT) symmetric non-Hermitian Hamiltonians can show real spectra in the PT sym-metry unbroken phase [3,4].


In this talk, I will introduce PT symmetric non-Hermitian systems and also discuss the important features of PT symmetric systems. I will show how NHQM provides powerful numerical and analytical tools for the study of various physical phenomena. I will finally present some experimental realizations of non-Hermitian systems.



1. P.A.M Dirac, The principles of quantum mechanics, Oxford University Press, 1981.

2. N. Moiseyev, “Non-Hermitian Quantum Mechanics”, Cambridge University Press, Cambridge, 2011.

3. Carl M Bender, “PT Symmetry: In Quantum and Classical Physics”, World Scientific Publishing Company, 2018.

4. Carl M Bender and Stefan Boettcher, “Real Spectra in non-Hermitian Hamiltonians Having PT Sym-metry,” Physical Review Letters 80, 5243 (1998).