Dirac's postulate of canonical quantization, [p̂i, q̂j] = ihδij for conjugate canonical variables, has been the most concise and general prescription on how to quantize a classical system. Since classical systems described by variables connected with canonical transformations are equivalent, [pδi, q̂j ] = ihδij must remain invariant under classical canonical transformations. This invariance has not been proved except for the limited class of cascaded infinitesimal transformations. In this paper it is shown that if (P̂i, Q̂j) are related to (p̂i, q̂j) by a classical canonical transformation, then [p̂i, q̂j] = ihδij implies [P̂i, Q̂j] = ihδij. In other words, the canonical quantization prescription is invariant for variables connected with classical canonical transformations.
|Number of pages||7|
|Journal||Chinese Journal of Physics|
|State||Published - Aug 2007|