Must a Hamiltonian be Hermitian? Export

@article{citeulike:791722, abstract = {A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space\&\#150;time reflection symmetry ( symmetry). Thus, there are infinitely many new Hamiltonians that one can construct that might explain experimental data. One would think that a quantum theory based on a non-Hermitian Hamiltonian violates unitarity. However, if symmetry is not broken, it is possible to use a previously unnoticed physical symmetry of the Hamiltonian to construct an inner product whose associated norm is positive definite. This construction is general and works for any -symmetric Hamiltonian. The dynamics is governed by unitary time evolution. This formulation does not conflict with the requirements of conventional quantum mechanics. There are many possible observable and experimental consequences of extending quantum mechanics into the complex domain, both in particle physics and in solid state physics. \©2003 American Association of Physics Teachers.}, author = {Bender, Carl M. and Brody, Dorje C. and Jones, Hugh F.}, citeulike-article-id = {791722}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000071000011001095000001&idtype=cvips&gifs=yes}, citeulike-linkout-1 = {http://link.aip.org/link/?AJP/71/1095}, citeulike-linkout-2 = {http://dx.doi.org/10.1119/1.1574043}, doi = {10.1119/1.1574043}, journal = {American Journal of Physics}, keywords = {non-hermitian\_hamiltonians, quantum\_physics}, number = {11}, pages = {1095--1102}, posted-at = {2008-02-25 19:09:26}, priority = {4}, publisher = {AAPT}, title = {Must a Hamiltonian be Hermitian?}, url = {http://dx.doi.org/10.1119/1.1574043}, volume = {71}, year = {2003} }

TY - JOUR ID - citeulike:791722 L3 - citeulike-article-id:791722 N2 - A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space–time reflection symmetry ( symmetry). Thus, there are infinitely many new Hamiltonians that one can construct that might explain experimental data. One would think that a quantum theory based on a non-Hermitian Hamiltonian violates unitarity. However, if symmetry is not broken, it is possible to use a previously unnoticed physical symmetry of the Hamiltonian to construct an inner product whose associated norm is positive definite. This construction is general and works for any -symmetric Hamiltonian. The dynamics is governed by unitary time evolution. This formulation does not conflict with the requirements of conventional quantum mechanics. There are many possible observable and experimental consequences of extending quantum mechanics into the complex domain, both in particle physics and in solid state physics. ©2003 American Association of Physics Teachers. IS - 11 JF - American Journal of Physics EP - 1102 TI - Must a Hamiltonian be Hermitian? PB - AAPT VL - 71 SP - 1095 KW - non-hermitian_hamiltonians KW - quantum_physics AU - Bender, Carl AU - Brody, Dorje AU - Jones, Hugh PY - 2003/// UR - http://dx.doi.org/10.1119/1.1574043 ER -