The vector and canonical components of the momentum operator in 3D Euclidean space spanned by general curvilinear coordinates

Shikakhwa M.

European Journal of Physics, cilt.47, sa.3, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1088/1361-6404/ae68c4
  • Dergi Adı: European Journal of Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO)
  • Anahtar Kelimeler: canonical momentum in curvilinear coordinates, Hermitian momentum operator, momentum in curvilinear coordinates
  • TED Üniversitesi Adresli: Evet

Özet

We construct the Hermitian vector and canonical components of the momentum operator in 3D Euclidean space spanned by general curvilinear coordinates (GCCs) using a simple, natural and unified approach based on identifying the momentum operator in any coordinate system as mass times the velocity operator. When this latter is calculated by applying the Heisenberg equation of motion, it returns ( (Formula presented) (Formula presented) times) the gradient operator plus an additional zero-valued sum, which when distributed among the components of the gradient, it makes each the Hermitian vector component of the momentum operator in GCCs. The canonical components follow immediately upon symmetrizing each of these vector components in the corresponding base vector. For accessability by wider audiences, we first develop the formalism for the simple polar coordinates (PCs) and then we develop the case for GCCs.