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CATEGORIES:Theoretical Physics Seminars
SUMMARY:Making sense of non-Hermitian Hamiltonians - Prof
Carl Bender
DTSTART:20120524T124500Z
DTEND:20120524T140000Z
UID:TALK761AT
URL:/talk/index/761
DESCRIPTION:The average quantum physicist on the street believ
es that a quantum-mechanical Hamiltonian must be D
irac Hermitian (invariant under combined matrix tr
ansposition and complex conjugation) in order to\n
guarantee that the energy eigenvalues are real and
that time evolution is unitary. However\, the Ham
iltonian H=p^{2} + i x^{3}\, which
is obviously not\nDirac Hermitian\, has a real po
sitive discrete spectrum and generates\nunitary ti
me evolution\, and thus it defines a fully consist
ent and\nphysical quantum theory!\n\nEvidently\, t
he axiom of Dirac Hermiticity is too restrictive.
While H=p^{2} + i x^{3}\, is not D
irac Hermitian\, it is PT symmetric\; that is\,\ni
nvariant under combined space reflection P and tim
e reversal T. The\nquantum mechanics defined by a
PT-symmetric Hamiltonian is a complex\ngeneralizat
ion of ordinary quantum mechanics. When quantum me
chanics is\nextended into the complex domain\, new
kinds of theories having strange\nand remarkable
properties emerge. In the past two years\, some of
these\nproperties have recently been verified in
laboratory experiments.\n\nA particularly interest
ing PT-symmetric Hamiltonian is H=p^{2}-x<
sup>4\, which\ncontains an upside-down poten
tial. We will discuss this potential in\ndetail\,
and explain in intuitive as well as in rigorous te
rms why the energy\nlevels of this potential are r
eal\, positive\, and discrete.
LOCATION:Theory Library
CONTACT:Dr Dimitri M Gangardt
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