Transactions in Theoretical and Mathematical Physics

Transactions in Theoretical and Mathematical Physics

On the coordinate representation in the Dirac bra-ket notation

Document Type : Original Article

Author
Mehdi Jafari Matehkolaee
Department of Physics, Amirkabir University of Technology (Tehran Polytechnic ), P.O.Box: 15875-4413,Tehran, Iran
10.30511/ttmp.2025.2065630.1060
Abstract
In this paper we discuss some traps which can occur in using Dirac bra-ket notation in the coordinate (or momentum) representation. Furthermore, we demonstrate that in order to avoid some misconceptions, it is necessary to distinguish the two operators. First, the ordinary derivative , is just the usual partial differentiation which acts on the scalar function; and should not be considered as an operator which can act on the vectors in the Hilbert space. Second, unbounded operator , which is usually mixed up with the former. Our discussion indicates that the action of these two operators is the same on bra position , but on ket it really leads to different results.
Keywords
Ordinary derivative
Dirac notation
Subjects
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Transactions in Theoretical and Mathematical Physics
Volume 2, Issue 3
Summer 2025
Pages 160-164

  • Receive Date 12 July 2025
  • Revise Date 15 July 2025
  • Accept Date 29 August 2025
  • First Publish Date 29 August 2025
  • Publish Date 01 August 2025