Tensors in Hilbert space

✍ Scribed by Nathan Rosen

• Publisher: Elsevier Science
• Year: 1969
• Tongue: English
• Weight: 343 KB
• Volume: 54
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1016/0003-4916(69)90158-4

✦ Synopsis

If one multiplies the Schriidinger wave function in the coordinate representation by the corresponding function in the momentum representation one gets a wave function which can be regarded as a mixed tensor in Hilbert space. This leads to a positivedefinite distribution function for the coordinate and the momentum. One can form a linear combination of such state tensors corresponding to a new kind of state. One can also form tensors describing non-observable states providing more information about the system than is permitted by quantum mechanics. Some generalizations are suggested, such as having the coordinate and momentum functions depend on different times.