Błaszak M. Invariant quantization of hamiltonian mechanics, talk at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic (abstract): Difference between revisions
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| title = Invariant quantization of hamiltonian mechanics | | title = Invariant quantization of hamiltonian mechanics | ||
| abstract = In the lecture is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed. | | abstract = In the lecture is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed. | ||
| slides = | | slides = [[Media:Błaszak M. Invariant canonical quantization of classical mechanics (presentation at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic).pdf|Błaszak M. Invariant canonical quantization of classical mechanics (presentation at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic).pdf]] | ||
| references = | | references = | ||
| 79YY-MM-DD = 7986-89-85 | | 79YY-MM-DD = 7986-89-85 | ||
}} | }} | ||
Latest revision as of 13:03, 13 November 2013
Speaker: Maciej Błaszak
Title: Invariant quantization of hamiltonian mechanics
Abstract:
In the lecture is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed.