Alternative momentum concept for a quantum mechanical particle in a box
For a particle in a box, the operator p[over ̂]=−i∂_{x} is not self-adjoint. We provide an alternative construction of a momentum operator p[over ̂]_{R}+ip[over ̂]_{I}, which has two self-adjoint components p[over ̂]_{R} and p[over ̂]_{I}. This leads to a description of momentum measurements perform...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-10-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.L042008 |
| Summary: | For a particle in a box, the operator p[over ̂]=−i∂_{x} is not self-adjoint. We provide an alternative construction of a momentum operator p[over ̂]_{R}+ip[over ̂]_{I}, which has two self-adjoint components p[over ̂]_{R} and p[over ̂]_{I}. This leads to a description of momentum measurements performed on a particle that is strictly limited to the interior of a box of size L, which yields quantized momentum values πn/L with n∈Z. |
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| ISSN: | 2643-1564 |