Introduction to PT-Symmetric Extensions of Quantum Mechanics

00:00 03-06-2008

'Courier New'; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: HE">Non-Hermitian  Hamiltonians  with  real  spectra  are
currently  an  active  field  of  research,  motivated both by the
necessity to understand  their  mathematical properties and by the
requirement  to  build  a consistent unitary quantum mechanics for
them.  A  particularly  important  subset  of  such  operators are
non-Hermitian  Hamiltonians   which  are  PT-symmetric,  such   as
H= p^2 + i x^3,  or  more  generally,  H = p^2 + x^2(ix)^n with  n
being a real parameter.   The  reality  of  the  spectrum of these
Hamiltonians  was  discovered  about  a  decade  ago by Bender and
Boettcher,  a  discovery  which initiated the recent  interest and
activity in this field.   This  talk  will  be  an introduction to
PT-symmetric quantum mechanics,  to its mathematical structure and
to possible applications.

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