BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:PT-symmetric quantum mechanics: Physics off the real axis - Profes
 sor Carl Bender: University of Washington in Saint Louis.
DTSTART:20241009T151500Z
DTEND:20241009T161500Z
UID:TALK220879@talks.cam.ac.uk
CONTACT:Amanda Stagg
DESCRIPTION:The average quantum physicist on the street would say that a\n
 quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under\nc
 ombined matrix transposition and complex conjugation) in order to\nguarant
 ee that the energy eigenvalues are real and that time evolution is\nunitar
 y. However\, the Hamiltonian $H=p^2+ix^3$\, which is obviously not\nDirac 
 Hermitian\, has a positive real discrete spectrum and generates\nunitary t
 ime evolution\, and thus it defines a fully consistent and physical\nquant
 um theory. Evidently\, the axiom of Dirac Hermiticity is too\nrestrictive.
  While $H=p^2+ix^3$ is not Dirac Hermitian\, it is PT symmetric\;\nthat is
 \, invariant under combined parity P (space reflection) and time\nreversal
  T. The quantum mechanics defined by a PT-symmetric Hamiltonian is\na comp
 lex generalization of ordinary quantum mechanics. When quantum\nmechanics 
 is extended into the complex domain\, new kinds of theories having\nstrang
 e and remarkable properties emerge. In the past few years\, some of\nthese
  properties have been verified in beautiful laboratory experiments. A\npar
 ticularly interesting PT-symmetric Hamiltonian is $H=p^2-x^4$\, which\ncon
 tains an upside-down potential. This potential is discussed in detail\,\na
 nd we explain in intuitive and in rigorous terms why the energy levels of\
 nthis potential are real\, positive\, and discrete.\n\n
LOCATION:MR3
END:VEVENT
END:VCALENDAR